The value of $\sin ^{2} 75^{\circ}-\sin ^{2} 15^{\circ}$ is:

$\sin ^{6} \theta+\cos ^{6} \theta$ is equal to

If $\theta$ is eliminated from the equations $x = a \cos(\theta - \alpha)$ and $y = b \cos(\theta - \beta)$,then $\frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{2xy}{ab} \cos(\alpha - \beta)$ is equal to

If $\sin A = \frac{1}{\sqrt{10}}$ and $\sin B = \frac{1}{\sqrt{5}}$,where $A$ and $B$ are positive acute angles,then $A + B = $

$\sin^{2} \theta = \frac{(x+y)^{2}}{4xy}$ is possible only when

If $\tan \theta + \cot \theta = 2$,then the value of $\tan^{100} \theta + \cot^{100} \theta$ is