The equation $\sin x \cos x = 2$ has

If $\sin x + \text{cosec } x = 2$,then $\sin^n x + \text{cosec}^n x$ is equal to

If $\tan x = \frac{2b}{a - c}$ $(a \ne c)$,$y = a \cos^2 x + 2b \sin x \cos x + c \sin^2 x$ and $z = a \sin^2 x - 2b \sin x \cos x + c \cos^2 x$,then:

Statement $(S1): \sin 55^{\circ} + \sin 53^{\circ} - \sin 19^{\circ} - \sin 17^{\circ} = \cos 2^{\circ}$.
Statement $(S2):$ The range of $\frac{1}{3 - \cos 2x}$ is $\left[\frac{1}{4}, \frac{1}{2}\right]$.
Which one of the following is correct?

If $a \cos 2\theta + b \sin 2\theta = c$ has $\alpha$ and $\beta$ as its solutions,then the value of $\tan \alpha + \tan \beta$ is

If $\cos \theta + \cos 7\theta + \cos 3\theta + \cos 5\theta = 0$,then $\theta$ is equal to: