If $5(\tan^2 x - \cos^2 x) = 2\cos 2x + 9$,then $\cos 4x$ is equal to

$\tan 81^{\circ}-\tan 63^{\circ}-\tan 27^{\circ}+\tan 9^{\circ}$ equals to

If $\tan A = \tan \alpha \coth x = \cot \beta \tanh x$,then $\tan (\alpha + \beta) =$

If $A$ lies in the third quadrant and $3 \tan A - 4 = 0,$ then $5 \sin 2A + 3 \sin A + 4 \cos A = $

Let $\alpha, \beta$ be two real numbers such that $\pi < (\alpha-\beta) < 3 \pi$. If $\sin \alpha+\sin \beta=\frac{-21}{65}$ and $\cos \alpha+\cos \beta=\frac{-27}{65}$,then $\cos \left(\frac{\beta-\alpha}{2}\right)=$

The number of $x \in [0, 2\pi]$ for which $|\sqrt{2 \sin^4 x + 18 \cos^2 x} - \sqrt{2 \cos^4 x + 18 \sin^2 x}| = 1$ is