Factorize the expression: $\sec ^2 x+5 \tan x+5$

The expression $\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is equal to

$\cos ^2(x)+\cos ^2\left(x+\frac{\pi}{3}\right)+\cos ^2\left(x-\frac{\pi}{3}\right) = $

If $A+B+C+D=2 \pi$,then $\cos A-\cos B+\cos C-\cos D=$

If $\cos(x) + \cos^2(x) = 1$,then $\sin^2(x) + \sin^4(x)$ is equal to

Let $S = \{x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) : 9^{1-\tan^2 x} + 9^{\tan^2 x} = 10\}$ and $\beta = \sum_{x \in S} \tan^2\left(\frac{x}{3}\right)$,then $\frac{1}{6}(\beta - 14)^2$ is equal to