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

Answer: (C)

$1$

it is Given that $\sin \theta +{\sin }^2\theta =1\Rightarrow \sin \theta =1-{\sin }^2\theta \Rightarrow \sin \theta ={\cos }^2\theta .............\left(1\right)$

Now, ${\cos }^2\theta +{\cos }^4\theta ={\cos }^2\theta +({\cos }^2\theta {)}^2={\cos }^2\theta +{\sin }^2\theta =1$ (from (1))

Therefore, Answer is $1$