The number of solutions of the equation $|\cot x|=\cot x+\frac{1}{\sin x}$ in the interval $[0,2 \pi]$ is

The number of solutions of the equation $32^{\tan ^{2} x}+32^{\sec ^{2} x}=81,0 \leq x \leq \frac{\pi}{4}$ is :

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

If ${\sin ^2}\theta - 2\cos \theta + \frac{1}{4} = 0,$ then the general value of $\theta $ is

No. of solution of equation $sin^{65}x\, -\, cos^{65}x =\, -1$ is, if $x \in (-\pi , \pi )$

All possible values of $\theta \in[0,2 \pi]$ for which $\sin 2 \theta+\tan 2 \theta>0$ lie in