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JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f(\theta)=3\left(\sin ^4\left(\frac{3 \pi}{2}-\theta\right)+\sin ^4(3 \pi+\theta)\right)-2\left(1-\sin ^2 2 \theta\right)\) and \(S=\left\{\theta \in[0, \pi]: f^{\prime}(\theta)=-\frac{\sqrt{3}}{2}\right\}\). If \(4 \beta=\sum_{\theta \in S} \theta\) then \(f(\beta)\) is equal to
- A \(\frac{11}{8}\)
- B \(\frac{5}{4}\)
- C \(\frac{9}{8}\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{l} f (\theta)=3\left(\sin ^4\left(\frac{3 \pi}{2}-\theta\right)+\sin ^4(3 x+\theta)\right)-2\left(1-\sin ^2 2 \theta\right) \\ S =\left\{\theta \in[0, \pi]: f ^{\prime}(\theta)=-\frac{\sqrt{3}}{2}\right\}\end{array}\)…
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