The number of solutions of the equation

Question:

The number of solutions of the equation

$1+\sin ^{4} x=\cos ^{2} 3 x, x \in\left[-\frac{5 \pi}{2}, \frac{5 \pi}{2}\right]$ is :

  1. 5

  2. 4

  3. 7

  4. 3


Correct Option: 1

Solution:

$1+\sin ^{4} x=\cos ^{2} 3 x$

$\sin x=0 \& \cos 3 x=1$

$0,2 \pi,-2 \pi,-\pi, \pi$

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