Question

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

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

Answer 1

Answer: (C)

$1$

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

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

Therefore, ${\cos }^2\theta +{\cos }^4\theta ={\cos }^2\theta (1+{\cos }^2\theta )$

$=\sin \theta (1+\sin \theta )$

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

$=1$