Let f(θ) = 3(sin^4(3π/2-θ))-2(1 -sin^2 2θ) and

Question

Let \(f(\theta)=3(sin^4(\frac{3\pi}{2}-\theta)+sin^4(3\pi+\theta))-2(1-sin^22\theta)\) and \(S=\{\theta ∈[0,\pi]:f'(\theta)=-\frac{\sqrt{3}}{2}\}.\) If 4β = \(\displaystyle\sum_{\theta∈s}^{}\theta,\) then f (β) is equal to

(1) 11/8

(2) 5/4

(3) 9/8

(4) 3/2

Answer 1

Correct option is (2) 5/4