If $\frac{\sin ^4 x}{2}+\frac{\cos ^4 x}{3}=\frac{1}{5},$ then
$(A)$ $\tan ^2 x=\frac{2}{3}$ $(B)$ $\frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{1}{125}$
$(C)$ $\tan ^2 x=\frac{1}{3}$ $(D)$ $\frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{2}{125}$
$(A,C)$
$(A,B)$
$(B,C)$
$(D,B)$
Find the degree measures corresponding to the following radian measures (Use $\pi=\frac{22}{7}$ ).
$\frac{11}{16}$
If $\sin \theta = - \frac{1}{{\sqrt 2 }}$ and $\tan \theta = 1,$ then $\theta $ lies in which quadrant
If $\cos (\alpha - \beta ) = 1$ and $\cos (\alpha + \beta ) = \frac{1}{e}$, $ - \pi < \alpha ,\beta < \pi $, then total number of ordered pair of $(\alpha ,\beta )$ is
If $x = a{\cos ^3}\theta ,y = b{\sin ^3}\theta ,$ then
If $\sin \theta + \cos \theta = 1$, then $\sin \theta \cos \theta = $