The variable $x$ satisfying the equation $\left| {\sin \,x\,\cos \,x} \right| + \sqrt {2 + {{\tan }^2}\,x + {{\cot }^2}\,x} = \sqrt 3$ belongs to the interval
$\left[ {0,\frac{\pi }{3}} \right]$
$\left( {\frac{\pi }{3},\frac{\pi }{2}} \right)$
$\left[ {\frac{{3\pi }}{4},\pi } \right)$
non-existent
The most general value of $\theta $ satisfying the equations $\sin \theta = \sin \alpha $ and $\cos \theta = \cos \alpha $ is
The number of solutions of the equation $\sin x=$ $\cos ^{2} x$ in the interval $(0,10)$ is
The number of $x \in [0,2\pi ]$ for which $\left| {\sqrt {2\,{{\sin }^4}\,x\, + \,18\,{{\cos }^2}\,x} - \,\sqrt {2\,{{\cos }^4}\,x\, + \,18\,{{\sin }^2}\,x} } \right| = 1$ is
If $4{\sin ^2}\theta + 2(\sqrt 3 + 1)\cos \theta = 4 + \sqrt 3 $, then the general value of $\theta $ is