Introduction to Trigonometry and Its Applications
NCERT Exemplar
CBSE
Grade 10
Question:
If $\sin \theta + \sin^2 \theta = 1$, then the value of $\cos^2 \theta + \cos^4 \theta$ is:
(a) $-1$
(b) $0$
(c) $1$
(d) $2$
Step-by-Step Solution
Key Concept: From $\sin \theta = 1 - \sin^2 \theta = \cos^2 \theta$, square both sides to get $\sin^2 \theta = \cos^4 \theta$.
Given $\sin \theta = 1 - \sin^2 \theta = \cos^2 \theta$. [0.5 Mark]
$\cos^2 \theta + \cos^4 \theta = \sin \theta + \sin^2 \theta = 1$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Deducing $\sin \theta = \cos^2 \theta$: 0.5 Mark
Substituting to get 1: 0.5 Mark
Correct Answer: $1$
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