Let $f(x) = sinx + 2sin^2x + 3sin^3x + 4sin^4x+....\infty $ , then number of solution $(s)$ of equation $f(x) = 2$ in $x \in \left[ { - \pi ,\pi } \right] - \left\{ { \pm \frac{\pi }{2}} \right\}$ is

If $\sin x=\frac{3}{5}, \cos y=-\frac{12}{13},$ where $x$ and $y$ both lie in second quadrant, find the value of $\sin (x+y)$.

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 $|\cos x|=\sin x$, such that $-4 \pi \leq x \leq 4 \pi$ is.

Find the principal solutions of the equation $\tan x=-\frac{1}{\sqrt{3}}.$

The number of distinct solutions of $\sec \theta \,\, + \,\,\tan \theta \, = \,\sqrt 3 \,,\,0\,\, \leqslant \,\,\theta \,\, \leqslant \,\,2\pi$