The value of $\tan \frac{\pi}{5} + 2 \tan \frac{2 \pi}{5} + 4 \cot \frac{4 \pi}{5}$ is

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

Consider the following two statements.
Statement $p$: The value of $\sin 120^\circ$ can be derived by taking $\theta = 240^\circ$ in the equation $2\sin \frac{\theta}{2} = \sqrt{1 + \sin \theta} - \sqrt{1 - \sin \theta}$.
Statement $q$: The angles $A, B, C$ and $D$ of any quadrilateral $ABCD$ satisfy the equation $\cos \left( \frac{1}{2}(A + C) \right) + \cos \left( \frac{1}{2}(B + D) \right) = 0$.
Then the truth values of $p$ and $q$ are respectively:

If $\sin x + \sin^{2} x = 1$,then the value of $\cos^{8} x + 2 \cos^{6} x + \cos^{4} x$ is

Evaluate: $\sin ^2 18^{\circ}+\sin ^2 24^{\circ}+\sin ^2 36^{\circ}+\sin ^2 42^{\circ}+\sin ^2 78^{\circ}+\sin ^2 90^{\circ}+\sin ^2 96^{\circ}+\sin ^2 102^{\circ}+\sin ^2 138^{\circ}+\sin ^2 162^{\circ}$

$\cos 12^{\circ} + \cos 60^{\circ} + \cos 84^{\circ} + \cos 132^{\circ} + \cos 156^{\circ} = $