If $\cos(x) + \cos^2(x) = 1$,then $\sin^2(x) + \sin^4(x)$ is equal to

The value of $\tan 20^{\circ} \tan 80^{\circ} \cot 50^{\circ} = $

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 $\cos A = -\frac{60}{61}$ and $\tan B = -\frac{7}{24}$ and neither $A$ nor $B$ is in the second quadrant,then the angle $A + \frac{B}{2}$ lies in the quadrant:

If $x \cos \theta = y \cos \left( \theta + \frac{2\pi}{3} \right) = z \cos \left( \theta + \frac{4\pi}{3} \right)$,then the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ is equal to

$3(\sin x-\cos x)^{4}+6(\sin x+\cos x)^{2}+4(\sin ^{6} x+\cos ^{6} x)$ is equal to