Let $\alpha$ and $\beta$ respectively be the maximum and the minimum values of the function
$f(\theta) = 4\left(\sin^4\left(\frac{7\pi}{2} - \theta\right) + \sin^4(11\pi + \theta)\right) - 2\left(\sin^6\left(\frac{3\pi}{2} - \theta\right) + \sin^6(9\pi - \theta)\right),; \theta \in \mathbb{R}.$
Then $\alpha + 2\beta$ is equal to:
🎥 Video solution / Text Solution of this question is given below:
$f(\theta) = 4(\cos^4\theta + \sin^4\theta) - 2(\cos^6\theta + \sin^6\theta)$
$= 4(1 - 2\sin^2\theta\cos^2\theta) - 2(1 - 3\sin^2\theta\cos^2\theta)$
$= 2 - \sin^2(2\theta)/2$
$\alpha = 2,; \beta = \frac{3}{2}$
$\Rightarrow \alpha + 2\beta = 2 + 3 = 5$