The greatest and least values of $\sin x \cos x$ are

Let $a$ be the maximum value of $(3 \cos \theta - 4 \sin \theta)$ and $\theta \neq \frac{n \pi}{2}$. If $\alpha = a \sin^2 \theta \cos^3 \theta$ and $\beta = a \sin^3 \theta \cos^2 \theta$,then $\sqrt{\frac{(\alpha^2 + \beta^2)^5}{(\alpha \beta)^4}} = $

What is the minimum value of $a \sec x + b \csc x$ for $0 < a < b$ and $0 < x < \pi/2$?

If $p = \sin^2 \theta + \cos^4 \theta$,then for all real values of $\theta$,which of the following is true?

Let $y=4 \sin^2 \theta - \cos 2 \theta$. If $l$ and $m$ are the minimum and maximum values of $y$ respectively,then

The minimum value of $27^{\cos 2x} 81^{\sin 2x}$ is.......