Question

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

• A. $-1$
• B. $1$
• C. $0$
• D. $2$

Answer 1

The correct option is B $1$

We have,

$\sin \theta +{\sin }^2\theta =1$

We know that

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

Therefore,

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

$\sin \theta -{\cos }^2\theta =0$

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

Since,

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

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

$=1$

Hence, the value is $1$.