$\sin (\pi + \theta )\sin (\pi - \theta )\csc^2 \theta = $

If the sides of a right-angled triangle are $\{\cos2\alpha + \cos2\beta + 2\cos(\alpha + \beta )\}$ and $\{\sin2\alpha + \sin2\beta + 2\sin(\alpha + \beta )\}$,then the length of the hypotenuse is:

If $A = \sin^2 x + \cos^4 x$,then for all real $x :$

If $m$ and $M$ are the minimum and the maximum values of $4 + \frac{1}{2} \sin^2 2x - 2 \cos^4 x$ for $x \in R$,then $M - m$ is equal to

$\tan 5x - \tan 3x - \tan 2x$ is equal to

Suppose $\theta$ and $\phi (\neq 0)$ are such that $\sec(\theta + \phi)$,$\sec\theta$,and $\sec(\theta - \phi)$ are in $A.P.$ If $\cos\theta = k \cos(\frac{\phi}{2})$ for some $k$,then $k$ is equal to