Question : If $2 \sin \theta+2 \sin ^2 \theta=2$, then the value of $2 \cos ^4 \theta+2 \cos ^2 \theta$ is:
Option 1: 4
Option 2: 2
Option 3: 1
Option 4: 0
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Correct Answer: 2
Solution :
Given: $2 \sin \theta+2 \sin ^2 \theta=2$
⇒ $2\sin\theta + 2\sin^2\theta = 2(\sin^2\theta + \cos^2\theta)$
⇒ $2\sin\theta + 2\sin^2\theta = 2\sin^2\theta + 2\cos^2\theta$
⇒ $2\sin\theta = 2\cos^2\theta$
⇒ $\sin\theta = \cos^2\theta$
Putting the value in the given equation,
$2 \cos ^4 \theta+2 \cos ^2 \theta$
$=2\sin^2\theta + 2\sin\theta = 2$
Hence, the correct answer is 2.
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