If $\sinh x = -\frac{4}{3}$,then $\sinh 2x + \cosh 2x = $

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:

Let $\alpha$ and $\beta$ be two real roots of the equation $(k+1) \tan^{2} x - \sqrt{2} \lambda \tan x = (1-k)$,where $k(\neq -1)$ and $\lambda$ are real numbers. If $\tan^{2}(\alpha+\beta) = 50$,then a value of $\lambda$ is:

If $\cos x + \cos^2 x = 1$,then the value of $\sin^2 x + \sin^4 x$ is

$\frac{1-\cos(2x)+\sin(x)}{\sin(2x)+\cos(x)} = $

$\cos \frac{7 \pi}{8}+\cos \frac{\pi}{4}+\cos \left(\frac{-\pi}{8}\right)-1=$