Trigonometric F...

Number of values of $$\theta \epsilon [0, 2\pi]$$ satisfying the equation $$\cot x-\cos x=1-\cot x.\cos x$$

The smallest positive integral value of p for which the equation $$\cos \left ( p\sin x \right )=\sin \left ( p\cos x \right )$$ in x has a solution in $$\left [ 0, 2\pi  \right ]$$ is

The number of solutions of equation $$5\sec \theta-13=12\tan \theta $$ in $$\left [ 0, 2\pi  \right ]$$ is

The number of solutions of the equation $$x^3+2x^2+5x+2 cos x=0$$ in $$[0, 2\pi]$$ is:

The number of solutions of the equation $$\tan x+\sec x=2\cos x$$ lying in the interval $$\left [ 0, 2\pi  \right ]$$ is

For each integer $$n>1$$, let $$S(n)$$ denote the number of solution of the equation $$\sin x=\sin nx$$ on the interval $$[0,\pi]$$ Find the value of $$S(2)+S(3)+S(4)$$.

If $$0\leq x\leq 2\pi $$, $$0\leq y\leq 2\pi $$ and $$\sin x+\sin y=2$$ then the value of $$x+y$$ is

If $$3\sin ^{2}\theta +2\sin ^{2}\phi=0 $$ and $$3\sin 2\theta +2\sin 2\phi=0$$, $$0< \theta < \frac{\pi }{2}$$ and $$0< \phi  < \frac{\pi }{2}$$, then the value of $$\theta +2\phi $$

if $$\displaystyle x,y\epsilon \left [ 0,2\pi  \right ]$$ and $$\displaystyle \sin x+\sin y=2$$ then the value of $$ x+y$$ is

The number of solutions of the equation $$\displaystyle  \cos 6x+\tan ^{2}x+\cos 6x\cdot \tan ^{2}x= 1$$ in the interval $$\displaystyle \left [ 0 ,2\pi  \right ]$$ is