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:

If $\tan B = \frac{n \sin A \cos A}{1 - n \cos^2 A}$,then $\tan(A + B)$ equals

For $0 < x \leq \pi$, $\sinh ^{-1}(\cot x)$ is equal to

Evaluate the expression: $\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{2 \pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{4 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\left(1+\cos \frac{6 \pi}{8}\right)\left(1+\cos \frac{7 \pi}{8}\right)$

Given that $\pi < \alpha < \frac{3\pi}{2}$,then the expression $\sqrt{4\sin^4 \alpha + \sin^2 2\alpha} + 4\cos^2 \left(\frac{\pi}{4} - \frac{\alpha}{2}\right)$ is equal to

The value of $\sin ^6(\theta) + \cos ^6(\theta) + 3 \sin ^2(\theta) \cos ^2(\theta)$ is