JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
Let \( \alpha \) and \( \beta \) respectively be the maximum and the minimum values of the function \( f(\theta)=4(\sin^{4}(\frac{7\pi}{2}-\theta)+\sin^{4}(11\pi+\theta)) - 2(\sin^{6}(\frac{3\pi}{2}-\theta)+\sin^{6}(9\pi-\theta)) \), \(\theta \in R\). Then \( \alpha+2\beta \) is equal to:
- A 4
- B 5
- C 3
- D 6
Answer & Solution
Correct Answer
(B) 5
Step-by-step Solution
Detailed explanation
\(f(\theta)=4\left(\sin ^4\left(\frac{7 \pi}{2}-\theta\right)+\sin ^4(11 \pi+\theta)\right)-2\left(\sin ^6\left(\frac{3 \pi}{2}-\theta\right)+\sin ^6(9 \pi-\theta)\right)\) \(f(\theta)=4\left(\cos ^4(\theta)+\sin ^4(\theta)\right)-2\left(\cos ^6 \theta+\sin ^6 \theta\right)\)…
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