Question

If $\sin \theta +{\sin }^2\theta =1$. Find the value of ${\cos }^2\theta +{\cos }^4\theta -1$.

• A. $1$
• B. $-1$
• C. $2$
• D. $0$

Answer 1

The correct option is D $0$

$\sin \theta +{\sin }^2\theta =1$
$\sin \theta =1-{\sin }^2\theta ={\cos }^2\theta$
Now put values in given equation, ${\cos }^2\theta +{\cos }^4\theta -1$
$\Rightarrow \sin \theta +{\sin }^2\theta -1=1-1=0[\because \sin \theta +{\sin }^2\theta =1]$.