Introduction to Trigonometry
RD Sharma
CBSE
Grade 10
Question:
If $\sin \theta + \sin^2 \theta = 1$, find the value of $\cos^2 \theta + \cos^4 \theta$.
Step-by-Step Solution
Key Concept: $\sin \theta = 1 - \sin^2 \theta = \cos^2 \theta \Rightarrow \cos^4 \theta = \sin^2 \theta \Rightarrow \cos^2 \theta + \cos^4 \theta = \sin \theta + \sin^2 \theta = 1$.
$\sin\theta = \cos^2\theta \Rightarrow \sin^2\theta = \cos^4\theta$. [1.0 Mark]
$\cos^2\theta + \cos^4\theta = \sin\theta + \sin^2\theta = 1$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Substituting $\cos^2 \theta = \sin \theta$: 1.0 Mark
Evaluating sum $= 1$: 1.0 Mark
Correct Answer:
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