If $\sin x + {\sin ^2}x = 1$, then the value of ${\cos ^{12}}x + 3{\cos ^{10}}x + 3{\cos ^8}x + {\cos ^6}x - 2$ is equal to
$0$
$1$
$-1$
$2$
Find the value of the trigonometric function $\tan \frac{19 \pi}{3}$.
If $\frac{\sin ^4 x}{2}+\frac{\cos ^4 x}{3}=\frac{1}{5},$ then
$(A)$ $\tan ^2 x=\frac{2}{3}$ $(B)$ $\frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{1}{125}$
$(C)$ $\tan ^2 x=\frac{1}{3}$ $(D)$ $\frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{2}{125}$
If $\sin A,\cos A$ and $\tan A$ are in $G.P.$, then ${\cos ^3}A + {\cos ^2}A$ is equal to
The value of $\cot \frac{\pi}{24}$ is :
The value of $\tan ( - 945^\circ )$ is