If $\cos A\sin \left( {A - \frac{\pi }{6}} \right)$ is maximum, then the value of $A$ is equal to
$\frac{\pi }{3}$
$\frac{\pi }{4}$
$\frac{\pi }{2}$
None of these
The number of solutions that the equation $sin5\theta cos3\theta = sin9\theta cos7\theta $ has in $\left[ {0,\frac{\pi }{4}} \right]$ is
If $\tan (\cot x) = \cot (\tan x),$ then $\sin 2x =$
Number of solution$(s)$ of the equation $\sin 2\theta + \cos 2\theta = - \frac{1}{2},\theta \in \left( {0,\frac{\pi }{2}} \right)$ 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 $\tan 2\theta \tan \theta = 1$, then the general value of $\theta $ is