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  4. The number of solutions of the equation 1+ sin4x = cos2 3x, x ∈ [- (5π/2), (5π/2)] is :

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Q. The number of solutions of the equation $1+\sin^{4}x = \cos^{2} 3x, x \in \left[- \frac{5\pi}{2}, \frac{5\pi}{2}\right] $ is :

JEE MainJEE Main 2019Trigonometric Functions

Solution:

$1+\sin^{4}x =\cos^{2}3x $
$ \sin x = 0 \& \cos3x = 1 $
$ 0, 2\pi , - 2\pi, - \pi , \pi $