The number of solutions of the pair of equations $ 2 \sin ^2 \theta-\cos 2 \theta=0 $, $ 2 \cos ^2 \theta-3 \sin \theta=0$ in the interval $[0,2 \pi]$ is
zero
one
two
four
The general solution of the trigonometric equation $\tan \theta = \cot \alpha $ is
General solution of $\tan 5\theta = \cot 2\theta $ is $($ where $n \in Z )$
If $tanA + cotA = 4$, then $tan^4A + cot^4A$ is equal to
$\tan \,{20^o}\cot \,{10^o}\cot \,{50^o}$ is equal to
The value of the expression
$\frac{{\left (sin 36^o + cos 36^o - \sqrt 2 sin 27^o)( {\sin {{36}^0} + \cos {{36}^0} - \sqrt 2 \sin {{27}^0}} \right)}}{{2\sin {{54}^0}}}$ is less than