Introduction to Trigonometry
RD Sharma
CBSE
Grade 10
Question:
If $\cos \theta + \cos^2 \theta = 1$, then the value of $\sin^2 \theta + \sin^4 \theta$ is:
(a) $1$
(b) $0$
(c) $-1$
(d) $2$
Step-by-Step Solution
Key Concept: $\cos \theta = 1 - \cos^2 \theta = \sin^2 \theta \Rightarrow \sin^4 \theta = \cos^2 \theta \Rightarrow \sin^2 \theta + \sin^4 \theta = \cos \theta + \cos^2 \theta = 1$.
$\cos \theta = \sin^2 \theta \Rightarrow \sin^2 \theta + \sin^4 \theta = \cos \theta + \cos^2 \theta = 1$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating sum $= 1$: 1.0 Mark
Correct Answer: $1$
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