The number of solutions to $\sin x=\frac{6}{x}$ with $0 \leq x \leq 12 \pi$ is

General solution of $eq^n\, 2tan\theta \, -\, cot\theta  =\, -1$ is

If$\cos 6\theta + \cos 4\theta + \cos 2\theta + 1 = 0$, where $0 < \theta < {180^o}$, then $\theta  =$

The expression $(1 + \tan x + {\tan ^2}x)$ $(1 - \cot x + {\cot ^2}x)$ has the positive values for $x$, given by

The roots of the equation $1 - \cos \theta = \sin \theta .\sin \frac{\theta }{2}$ is

The only value of $x$ for which ${2^{\sin x}} + {2^{\cos x}} > {2^{1 - (1/\sqrt 2 )}}$ holds, is