$\cot x - \tan x = $

If $\csc \theta = \frac{p + q}{p - q}$,then $\cot \left( \frac{\pi}{4} + \frac{\theta}{2} \right) = $

If $\alpha$ and $\beta$ are solutions of $\sin^2 x + a \sin x + b = 0$ as well as $\cos^2 x + c \cos x + d = 0$,then $\sin(\alpha + \beta)$ is equal to

If $x=a(\sin \theta+\cos \theta)$ and $y=b(\sin \theta-\cos \theta)$,then the value of $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}$ is

If $x \cos \theta = y \cos \left( \theta + \frac{2\pi}{3} \right) = z \cos \left( \theta + \frac{4\pi}{3} \right)$,then the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ is equal to

Let $E = \left( {1 - \frac{{\cos 61^\circ}}{{\cos 1^\circ}}} \right) \left( {1 - \frac{{\cos 62^\circ}}{{\cos 2^\circ}}} \right) \dots \left( {1 - \frac{{\cos 119^\circ}}{{\cos 59^\circ}}} \right)$,then $E$ is equal to: