Assignment: Trigonometric Equations

Assignment: Determinants

Date: 19th December, 2009

Batch: Target1. Evaluate

2. Let be a repeated root of the quadratic equation be the polynomials of degrees 3, 4, and 5 resp. Show that is divisible by , where prime denotes the derivative with respect to x. 3. If then prove that and that , where S denotes the sum of cofactors of all the elements in 4. For what real values of k, the system of equations has a solution? Find the solutions5. For what values of a and b, the following system of equations is consistent?

6. Solve the following system of equations: , where

7. Consider the system of linear equations Find the values of for which this system has non-trivial solutions8. If a, b, c are distinct real numbers, and the system of equations has a non-trivial solution, show that

9. If A, B, C are the angles of a triangle ABC and the system of linear equations

has a non-trivial solution,

prove that 10. Find X and Y, if

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