The solution set of the equation $tan(\pi\, tanx) = cot(\pi\, cot\, x)$ is
$\phi $
$\{0\}$
$\left\{ {\frac{\pi }{4}} \right\}$
none of these
The number of solutions of the equation $\sqrt[3]{{\sin \theta - 1}} + \sqrt[3]{{\sin \theta }} + \sqrt[3]{{\sin \theta + 1}} = 0$ in $[0,4\pi]$ is
If $5{\cos ^2}\theta + 7{\sin ^2}\theta - 6 = 0$, then the general value of $\theta $ is
If $cosx + secx =\, -2$, then for a $+ve$ integer $n$, $cos^n x + sec^n x$ is
Statement $-1:$ The number of common solutions of the trigonometric equations $2\,sin^2\,\theta - cos\,2\theta = 0$ and $2 \,cos^2\,\theta - 3\,sin\,\theta = 0$ in the interval $[0, 2\pi ]$ is two.
Statement $-2:$ The number of solutions of the equation, $2\,cos^2\,\theta - 3\,sin\,\theta = 0$ in the interval $[0, \pi ]$ is two.
If $1\,\, + \,\,\sin \theta \,\, + \,\,{\sin ^2}\theta + \ldots .\,\,to\,\,\infty \,\, = \,\,4\, + 2\sqrt 3 ,\,\,0\,\, < \,\theta \,\,\pi ,\,\,\theta \,\, \ne \,\frac{\pi }{2}\,,$ then $\theta = $