If $\sqrt{3}\left(\cos ^{2} x\right)=(\sqrt{3}-1) \cos x+1,$ the number of solutions of the given equation when $x \in\left[0, \frac{\pi}{2}\right]$ is

The number of points in $(-\infty, \infty)$, for which $x^2-x \sin x-\cos x=0$, is

If $tanA + cotA = 4$, then $tan^4A + cot^4A$ is equal to

The number of solutions of $sin \,3x\, = cos\, 2x$ , in the interval $\left( {\frac{\pi }{2},\pi } \right)$ is

The value of $\theta $ satisfying the given equation $\cos \theta + \sqrt 3 \sin \theta  = 2,$ is

Number of solutions to the system of equations $sin \frac{x+y}{2}=0$ and $|x| + |y| = 1$