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

If $\cot x=-\frac{5}{12}, x$ lies in second quadrant, find the values of other five trigonometric functions.

Find the values of other five trigonometric functions if $\cot x=\frac{3}{4}, x$ lies in third quadrant.

Prove that: $\frac{(\sin 7 x+\sin 5 x)+(\sin 9 x+\sin 3 x)}{(\cos 7 x+\cos 5 x)+(\cos 9 x+\cos 3 x)}=\tan 6 x$

Find the value of the trigonometric function $\sin 765^{\circ}$

$\tan 1^\circ \tan 2^\circ \tan 3^\circ \tan 4^\circ ........\tan 89^\circ = $