Question

If $\sin \theta +{\sin }^2\theta =1,$ then ${\cos }^2\theta +{\cos }^4\theta =$

• A. $1$
• B. $\sqrt{2}$
• C. $0$
• D. $2$

Answer 1

The correct option is A $1$

Given: $\sin \theta +{\sin }^2\theta =1$
$\therefore \sin \theta =1-{\sin }^2\theta$
$\therefore \sin \theta ={\cos }^2\theta$
Now, ${\cos }^2\theta +{\cos }^4\theta$ $=\sin \theta +{\sin }^2\theta =1$