Trigonometric Equations

If  $-\frac{\pi }{2}\le x\le \frac{\pi }{2}$, then number of the points of intersection of the given curves $y=\cos x$, $y=\sin 3x$ is/are

If  $\tan \left(\pi \cos \theta \right)=\cot (\pi \sin \theta ),$ then $\sin \left(\theta +\frac{\pi }{4}\right)$ can be equal to

If  $\text{x}\in \left(-\pi \text{, }\pi \right)$ then the number of solutions of the equation  $2^{1+\left|\cos x\right|+\left|{\cos }^{2}x\right|+\mathrm{...}}\mathrm{}$ = 4 is/are-

Find the domain of trigonometric equation $y=\sqrt{\tan x}$ in $\left[0,2\mathrm{\pi }\right]$.

Find the domain of trigonometric equation $y=\sqrt{\mathrm{cosec}x}$ in $\left[0,2\mathrm{\pi }\right]$.

Find the domain of trigonometric equation $y=\sqrt{\sec x}$ in $\left[0,2\mathrm{\pi }\right]$.

Find the domain of trigonometric equation $y=\sqrt{\cos x}$ in $\left[0,2\mathrm{\pi }\right]$.

General solutions of $\sin x=-\frac{\sqrt{3}}{2}$ and $\cos x=\frac{-1}{2}$ are equal.

General solutions of $\sin x=\frac{-1}{\sqrt{2}}$ and $\cos x=\frac{-1}{\sqrt{2}}$ are equal.

General solutions of $\sin x=\frac{1}{\sqrt{2}}$ and $\cos x=\frac{1}{\sqrt{2}}$ are equal.

General solutions of $\sin x=\frac{\sqrt{3}}{2}$ and $\cos x=\frac{1}{2}$ are equal.

Find the domain of $\sin \frac{x}{2}+\cos \frac{x}{2}$.

Find the domain of $\sin x+4\cos x$.

Find the domain of $\sin 2x-3\cos x$.

Find the domain of $\sin 2x+\cos x$.