Let f(θ) = 3 (sin^4 ((3π)/2 - θ ) + sin^4(3π + θ) ) - 2(1 - sin^2 2θ) and S = \θ ∈ [0, π] : f'(θ) = -frac√(3)2 \. If 4β = sum_θ ∈ S θ, then f(β) is equal to

Let f(θ) = 3 (sin^4 ((3π)/2 - θ ) + sin^4(3π + θ) ) - 2(1 -… — JEE Main 2023 Mathematics PYQ

JEE Main 2023 · 29 Jan · Shift 1

Let

f(\theta) = 3\left(\sin^4\left(\frac{3\pi}{2} - \theta\right) + \sin^4(3\pi + \theta)\right) - 2(1 - \sin^2 2\theta)

and

S = \left\{\theta \in [0, \pi] : f'(\theta) = -\frac{\sqrt{3}}{2}\right\}

. If

4\beta = \sum_{\theta \in S} \theta

, then

f(\beta)

is equal to

Show answer

Correct option: A

[JEE Main 2023 · 29 Jan · Shift 1]

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