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The number of solutions of the equation ...

The number of solutions of the equation ` 1 +sin^(4) x = cos ^(2) 3x, x in [-(5pi)/(2),(5pi)/(2)]` is

A

7

B

3

C

4

D

5

Text Solution

Verified by Experts

The correct Answer is:
D
`1+sin^(4)xn =cos^(2)3x," "sin^(4)x=-sin^(4)3x`
Then solution will exist only if
`sin^(4)x=0 and sin^(4)x=0 and sn^(2)3x=0`
`x=nx" or "3x=mpi" "m_(1)n in z`
i.e., `x=0, pi, 2pi, pi, -2pi` are 5 solution is `[(-5pi)/(2),(5p)/(2)]`
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