Question : For any acute angle $\theta, \sin \theta+\sin^2 \theta=1$, then the value of $\cos^2 \theta+\cos^4 \theta=$___________.
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: –1
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Correct Answer: 1
Solution :
Given:
$\sin \theta+\sin ^2 \theta=1$
⇒ $\sin\theta = 1- \sin^2\theta$
⇒ $\sin \theta = \cos^2\theta$
$\cos^2 \theta+\cos^4 \theta= \sin\theta + \sin^2\theta = 1$
Hence, the correct answer is 1.
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