If $\frac{2 \sin \alpha}{1+\cos \alpha+\sin \alpha}=x$,then $\frac{1-\cos \alpha-\sin \alpha}{\cos \alpha}=$

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

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

If $\theta$ is an acute angle and $2 \sin ^2 \theta = \cos ^4 \frac{\pi}{8} + \sin ^4 \frac{3 \pi}{8} + \cos ^4 \frac{5 \pi}{8} + \sin ^4 \frac{7 \pi}{8}$,then $\theta =$

$\sum_{k=0}^4 \sin^2 \left( (2k+1) \frac{\pi}{20} \right) =$

The expression $\cos^2(A - B) + \cos^2 B - 2\cos(A - B)\cos A\cos B$ is