Question

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

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is C $1$

$\because \sin \theta +{\sin }^2\theta =1$
$\Rightarrow \sin \theta =1-{\sin }^2\theta ={\cos }^2\theta$
Squaring both sides
${\sin }^2\theta ={\cos }^4\theta$
${\cos }^2\theta ={\cos }^4\theta$
${\cos }^2\theta +{\cos }^4\theta ={\cos }^2\theta +{\sin }^2\theta =1$