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

Let $x \in [0, 6\pi]$ satisfy the equation $\cos x - \sin x = -1$. If $x = k(\frac{\pi}{3})$ where $k \in \mathbb{N}$, then find the number of possible values of $k$.

If $3 \cos x \neq 2 \sin x$,then the general solution of $\sin ^{2} x-\cos 2 x=2-\sin 2 x$ is

If $\cot \frac{x}{2} - \operatorname{cosec} \frac{x}{2} = \cot x$,then the values of $x$ are

The number of solutions of $8 \cos x = x$ will be:

If $\theta$ and $\alpha$ are not odd multiples of $\frac{\pi}{2}$,then $\tan \theta = \tan \alpha$ implies the general solution is