Question

Let \( \alpha \) and \( \beta \) respectively be the maximum and the minimum values of the function \( f(\theta) = 4\left(\sin^4\left(\frac{7\pi}{2} - \theta\right) + \sin^4(11\pi + \theta)\right) - 2\left(\sin^6\left(\frac{3\pi}{2} - \theta\right) + \sin^6(9\pi - \theta)\right) \). Then \( \alpha + 2\beta \) is equal to :

• A. 4
• B. 3
• C. 5
• D. 6

Hint:

The expression \( a(\sin^4 x + \cos^4 x) + b(\sin^6 x + \cos^6 x) \) is a very common JEE pattern. Always simplify it down to a function of \( \sin^2(2x) \).

Answer 1

The Correct Option is C