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Mathematics Question on Trigonometric Equations

Let f(θ)=3[sin4(3π2−θ)+sin4(3π+θ)]−2(1−sin22θ)f(\theta)=3[sin^4(\frac{3\pi}{2}-\theta)+sin^4(3\pi+θ)]-2(1-sin^22\theta) and S=θ∈[0,π]:f′(θ)=−32S=\\{\theta∈[0,\pi]:f'(\theta)=-\frac{\sqrt3}{2}\\}. If 4β∑θ∈Sθ4\beta \sum_{\theta∈S}\theta, then f(β)f(\beta) is equal to

A

9/8

B

3/2

C

5/4

D

11/8

Answer

5/4

Explanation

Solution

The correct answer is 5/4