Solve $\cos x=\frac{1}{2}$

The sum of all $x \in[0, \pi]$ which satisfy the equation $\sin x+\frac{1}{2} \cos x=\sin ^2\left(x+\frac{\pi}{4}\right)$ is

The smallest positive values of $x$ and $y$ which satisfy $\tan (x - y) = 1,\,$ $\sec (x + y) = \frac{2}{{\sqrt 3 }}$ are

The number of integral value $(s)$ of $'p'$ for which the equation $99\cos 2\theta  - 20\sin 2\theta  = 20p + 35$ , will have a solution is 

If $\sec 4\theta - \sec 2\theta = 2$, then the general value of $\theta $ is

The number of solutions of the equation $\sin x=$ $\cos ^{2} x$ in the interval $(0,10)$ is