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

The equation $3{\sin ^2}x + 10\cos x - 6 = 0$ is satisfied, if

If $|cos\ x + sin\ x| + |cos\ x\ -\ sin\ x| = 2\ sin\ x$ ; $x \in  [0,2 \pi ]$ , then maximum integral value of $x$ is

The solution of the equation $4{\cos ^2}x + 6$${\sin ^2}x = 5$

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

The equation $\sqrt 3 \sin x + \cos x = 4$ has