Question

Choose the correct answer from the alternatives given.
If $\sin +{\sin }^2\theta =1,$ then ${\cos }^2\theta +{\cos }^4\theta$ is equal to

Answer 1

Given, $\sin \theta +{\sin }^2\theta =1.$

$\sin \theta =1-{\sin }^2\theta ={\cos }^2\theta$

$\sin \theta ={\cos }^2\theta$

${\sin }^2\theta ={\cos }^4\theta$

$As,\sin \theta +{\sin }^2\theta .$

$\therefore {\cos }^2\theta +{\cos }^4\theta =1$