If $\tan A + \cot A = 2$,then the value of $\tan^{4} A + \cot^{4} A$ is:

If $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7} = \frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}$,then $\sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14} \sin \frac{7 \pi}{14} \sin \frac{9 \pi}{14} \sin \frac{11 \pi}{14} \sin \frac{13 \pi}{14} = $

If $\frac{5 \sinh 2x}{7+6 \cosh 2x} = \frac{3}{2}$,then $3 \tanh^2 x + 20 \tanh x = $

$\cos ^3\left(\frac{\pi}{8}\right) \cos \left(\frac{3 \pi}{8}\right)+\sin ^3\left(\frac{\pi}{8}\right) \sin \left(\frac{3 \pi}{8}\right) = $

The value of $\cos ^2 76^{\circ}+\cos ^2 16^{\circ}-\cos 76^{\circ} \cos 16^{\circ}$ is equal to

If $A(n) = \sin^n \alpha + \cos^n \alpha$,then $A(1) A(4) + A(2) A(5) =$