The number of solutions of the equation $x +2 \tan x =\frac{\pi}{2}$ in the interval $[0,2 \pi]$ is :

The number of solutions of the equation $\sin \theta+\cos \theta=\sin 2 \theta$ in the interval $[-\pi, \pi]$ is

If $\left| {\,\begin{array}{*{20}{c}}{\cos (A + B)}&{ - \sin (A + B)}&{\cos 2B}\\{\sin A}&{\cos A}&{\sin B}\\{ - \cos A}&{\sin A}&{\cos B}\end{array}\,} \right| = 0$, then $B =$

The number of solutions of $tan\, (5\pi\, cos\, \theta ) = cot (5 \pi \,sin\, \theta )$ for $\theta$ in $(0, 2\pi )$ is :

Find the principal and general solutions of the equation $\sec x=2$

If $\sin \theta + \cos \theta = 1$ then the general value of $\theta $ is