Question : If $\sin \theta+\sin ^2 \theta=1$, then the value of $\cos ^2 \theta+\cos ^4 \theta$ is equal to:
Option 1: 5
Option 2: $\frac{1}{2}$
Option 3: $1$
Option 4: $0$
Correct Answer: $1$
Solution :
Given: $\sin \theta+\sin ^2 \theta=1$
Use the trigonometric identity, $\sin^2 \theta+\cos^2 \theta=1$.
$\sin \theta+\sin ^2 \theta=1$
⇒ $\sin \theta=1–\sin ^2 \theta$
⇒ $\sin \theta=\cos ^2 \theta$
The value of $\cos ^2 \theta+\cos ^4 \theta=\sin \theta+\sin^2 \theta =1$.
Hence, the correct answer is 1.
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