QJEEM19Ma2a13: JEE Main 2019 Mathematics - Class 11 JEEM19Ma2a13 Solution: The number of solutions of the equation 1 + sin 4 x = cos 2 3x, …

Question

Verified Solution • 2025–26 Session moderate

The number of solutions of the equation
1 + sin⁴ x = cos²3x,

x \in [- \frac{5 π}{2}, \frac{5 π}{2}]

is :

Accepted Answer

\underset{\geq 1}{\underset{―}{1 + \sin^{4} x}} = \underset{\leq 1}{\underset{―}{\cos^{2} 3 x}}

Now for equality to hold sin⁴x = 0 & cos²3x = 1

sin⁴ = 0

\Rightarrow

x = -2

π

, -

π

, 0,

π

, 2

π

All of which satisfy cos²3x = 1

\Rightarrow

5 solutions

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