If $\sin x + \cos x = \frac{1}{5},$ then $\tan 2x$ is

If $a\tan \theta = b$, then $a\cos 2\theta + b\sin 2\theta = $

If $\sin \theta + \cos \theta = x,$ then ${\sin ^6}\theta + {\cos ^6}\theta = \frac{1}{4}[4 - 3{({x^2} - 1)^2}]$ for

The value of $\frac{1}{4} \,\,tan \frac{\pi}{8} +\frac{1}{8} \,\,tan \frac{\pi}{16}+\frac{1}{16} \,\,tan \frac{\pi}{32}+.\,.\,.\,\infty  $ terms is equal to-

$\tan \frac{A}{2}$ is equal to

Which of the following functions have the maximum value unity ?