First slide

Trigonometric equations

Question

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

Moderate

A

3
B

5
C

7
D

4

Solution

$The equation holds good if L H S = R H S = 1$
$\sin^{4} x = 0, \cos^{2} 3 x = 1$
$∴ x = π, 2 π, 0, - π, - 2 π$

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