If $\frac{\sin ^4 x}{2}+\frac{\cos ^4 x}{3}=\frac{1}{5},$ then

$(A)$ $\tan ^2 x=\frac{2}{3}$ $(B)$ $\frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{1}{125}$

$(C)$ $\tan ^2 x=\frac{1}{3}$ $(D)$ $\frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{2}{125}$

  • [IIT 2009]
  • A

    $(A,C)$

  • B

    $(A,B)$

  • C

    $(B,C)$

  • D

    $(D,B)$

Similar Questions

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

  • [IIT 2005]

If $x = a{\cos ^3}\theta ,y = b{\sin ^3}\theta ,$ then

If $\sin \theta + \cos \theta = 1$, then $\sin \theta \cos \theta = $