11X1 T07 02 sum & difference of angles (2011)
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Transcript of 11X1 T07 02 sum & difference of angles (2011)
![Page 1: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/1.jpg)
Sum & Difference of Angles
![Page 2: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/2.jpg)
Sum & Difference of Anglesy
x
1
![Page 3: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/3.jpg)
Sum & Difference of Anglesy
x
1
P
![Page 4: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/4.jpg)
Sum & Difference of Anglesy
x
1
P
![Page 5: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/5.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
![Page 6: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/6.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
cos ,sin
![Page 7: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/7.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
![Page 8: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/8.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
![Page 9: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/9.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
![Page 10: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/10.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
2 2 21 1 2 1 1 cosPQ
![Page 11: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/11.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ
![Page 12: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/12.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ
By coordinate geometry
![Page 13: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/13.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ
2 22 cos cos sin sinPQ
By coordinate geometry
![Page 14: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/14.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ
2 22 cos cos sin sinPQ 2 2 2 2 2cos 2cos cos cos sin 2sin sin sinPQ
By coordinate geometry
![Page 15: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/15.jpg)
Sum & Difference of Anglesy
x
1
P
1
x
y
cos1x
cosx
sin1
sin
y
y
cos ,sin
Q cos ,sin
By trigonometry
2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ
2 22 cos cos sin sinPQ 2 2 2 2 2cos 2cos cos cos sin 2sin sin sinPQ
By coordinate geometry
2 2 2cos cos 2sin sinPQ
![Page 16: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/16.jpg)
2 2cos 2 2cos cos 2sin sin
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2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
![Page 18: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/18.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
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2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
![Page 20: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/20.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
![Page 21: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/21.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
![Page 22: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/22.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin
![Page 23: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/23.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin
sinsincoscoscos
![Page 24: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/24.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
sinsincoscoscos
![Page 25: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/25.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
sinsincoscoscos
![Page 26: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/26.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
sinsincoscoscos
![Page 27: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/27.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
sinsincoscoscos
![Page 28: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/28.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
sinsincoscoscos
![Page 29: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/29.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
If it’s not the sine
sinsincoscoscos
![Page 30: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/30.jpg)
2 2cos 2 2cos cos 2sin sin
cos cos cos sin sin
Replace with
cos cos cos sin sin
cos cos (even function i.e. )f x f x
sin sin (odd function i.e. )f x f x
cos cos cos sin sin cos, cos, sin, sin
If it’s not the sine,it’s not the sign
sinsincoscoscos
![Page 31: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/31.jpg)
Replace with 90
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Replace with 90
cos 90 cos 90 cos sin 90 sin
![Page 33: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/33.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
![Page 34: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/34.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
![Page 35: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/35.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with
![Page 36: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/36.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
![Page 37: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/37.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
![Page 38: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/38.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
![Page 39: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/39.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
![Page 40: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/40.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
![Page 41: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/41.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
![Page 42: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/42.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
![Page 43: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/43.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
![Page 44: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/44.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
If it’s the sine
![Page 45: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/45.jpg)
Replace with 90
cos 90 cos 90 cos sin 90 sin
cos 90 cos 90 cos sin 90 sin
sin sin cos cos sin
Replace with sin sin cos cos sin
sin sin cos cos sin
sincoscossinsin
sin, cos, cos, sin
If it’s the sine,it’s the sign
![Page 46: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/46.jpg)
tan
![Page 47: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/47.jpg)
tan
sin
tancos
![Page 48: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/48.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
![Page 49: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/49.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos
![Page 50: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/50.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos
tan tantan1 tan tan
![Page 51: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/51.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos
tan tantan1 tan tan
Replace with
![Page 52: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/52.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos
tan tantan1 tan tan
Replace with
tan tantan
1 tan tan
![Page 53: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/53.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos
tan tantan1 tan tan
Replace with
tan tantan
1 tan tan
tan tan
(odd function i.e. )f x f x
![Page 54: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/54.jpg)
tan
sin
tancos
sin cos cos sintancos cos sin sin
sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos
tan tantan1 tan tan
Replace with
tan tantan
1 tan tan
tan tan
(odd function i.e. )f x f x tan tantan
1 tan tan
![Page 55: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/55.jpg)
tantan1tantantan
![Page 56: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/56.jpg)
tan plus tan
tantan1tantantan
![Page 57: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/57.jpg)
tan plus tan
on one minus tan, tan
tantan1tantantan
![Page 58: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/58.jpg)
tan plus tan
on one minus tan, tan
tantan1tantantan
Sum and Difference of Angles
![Page 59: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/59.jpg)
tan plus tan
on one minus tan, tan
tantan1tantantan
Sum and Difference of Angles
sincoscossinsin
![Page 60: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/60.jpg)
tan plus tan
on one minus tan, tan
tantan1tantantan
Sum and Difference of Angles
sincoscossinsin
sinsincoscoscos
![Page 61: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/61.jpg)
tan plus tan
on one minus tan, tan
tantan1tantantan
Sum and Difference of Angles
sincoscossinsin
sinsincoscoscos
tantan1tantantan
![Page 62: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/62.jpg)
e.g. i Expand cos 2 3
![Page 63: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/63.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3
![Page 64: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/64.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
![Page 65: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/65.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
![Page 66: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/66.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
![Page 67: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/67.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
13
![Page 68: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/68.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
13
(iii) Find the exact value of sin15
![Page 69: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/69.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
13
(iii) Find the exact value of sin15
sin15 sin 45 30
![Page 70: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/70.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
13
(iii) Find the exact value of sin15
sin15 sin 45 30
sin 45 cos30 cos 45 sin30
![Page 71: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/71.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
13
(iii) Find the exact value of sin15
sin15 sin 45 30
sin 45 cos30 cos 45 sin30
1 3 1 12 22 2
![Page 72: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/72.jpg)
e.g. i Expand cos 2 3
cos 2 3 cos 2 cos3 sin 2 sin 3 tan 20 tan10(ii) Simplify
1 tan 20 tan10
tan 20 tan10 tan 20 101 tan 20 tan10
tan30
13
(iii) Find the exact value of sin15
sin15 sin 45 30
sin 45 cos30 cos 45 sin30
1 3 1 12 22 2
3 1
2 2
![Page 73: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/73.jpg)
2 1iv If sin and cos , find sin3 4
![Page 74: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/74.jpg)
2 1iv If sin and cos , find sin3 4
23
5
![Page 75: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/75.jpg)
2 1iv If sin and cos , find sin3 4
23
5
1
4 15
![Page 76: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/76.jpg)
2 1iv If sin and cos , find sin3 4
23
5
1
4 15
sin sin cos cos sin
![Page 77: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/77.jpg)
2 1iv If sin and cos , find sin3 4
23
5
1
4 15
sin sin cos cos sin
2 1 5 153 4 3 4
![Page 78: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/78.jpg)
2 1iv If sin and cos , find sin3 4
23
5
1
4 15
sin sin cos cos sin
2 1 5 153 4 3 4
2 5 3
12
![Page 79: 11X1 T07 02 sum & difference of angles (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081401/559f77931a28abb4418b4684/html5/thumbnails/79.jpg)
2 1iv If sin and cos , find sin3 4
23
5
1
4 15
sin sin cos cos sin
2 1 5 153 4 3 4
2 5 3
12
Exercise 14D; 1ade, 2bce, 5ac, 7, 9ac, 10ac, 12, 13ac, 16ab, 17, 23