Assignment: Trigonometry Ratios and Identities Date: 20th August, 2009

1. (R-34.10-2)If sin +sin2 = 1, then find the value of cos12 + 3cos10 + 3cos8 + cos6 -1

2. (R-34.17-25) If ax/cos + by/sin = a2 –b2, and axsin/cos2 - bycos/sin2 = 0, prove that (ax)2/3 + (by)2/3 = (a2-b2)2/3

3. (R-34.19-32) If exp{(sin2x + sin4x + sin6x + ………so on)loge3} satisfies the equation x2 – 28x +27 =0, find the value of cosx/(cosx + sinx) , 0<x</2

4. (B-ex1-2) Prove that: cos2A = 2sin2B + 4cos(A+B)sinAsinB + cos(2A+2B)5. (B-ex1-3) Prove that: tanA + 2tan2A + 4tan4A +8cot8A = cotA6. (B-ex1-4b) Prove that: tan9 – tan27 – tan63 + tan81 = 47. (B-ex1-5) If X = sin( +7/12) + sin( - /12) + sin( +3/12), Y= cos(+7/12) +cos(-/12) +cos(+3/12)

then prove that X/Y – Y/X = 2tan28. (B-ex1-6) find the positive integers p,q,r,s satisfying tan/24 = (p - q)( r -

s)9. (B-ex1-10) If the value of expression sin25 sin35 sin85 can be expressed as

(a+b)/c, where a,b,c N and are in their lowest form, find the value of (a+b+c)

10. (B-ex1-12) Prove that 4cos(2/7) cos(/7) – 1 = 2cos(2/7)11. (B-ex1-18a) Calculate: 4cos20 – 3 cot20 12. (B-ex1-18b) Calculate: (2cos40 – cos20)/sin2013. (B-ex1-18d) Caculate: tan10 – tan50 + tan7014. (B-ex1-19) Given that (1+tan1)(1+tan2)……..(1+tan45) = 2n, find n.15. (B-ex1-21) If A+B+C = and cot = cotA+cotB+cotC, show that

sin(A-) sin(B-) sin(C-) = sin316. (B-ex1-24) In a right angled triangle, acute angles A and B satisfytanA + tanB +tan2A + tan2B +tan3A +tan3B = 70find the angle A and B in radians.