Introduction to Trigonometry
RD Sharma
CBSE
Grade 10
Question:
If $\sin \theta = \cos \theta$ for an acute angle $\theta$, then $2 \tan^2 \theta + \sin^2 \theta - 1$ is:
(a) $\dfrac{3}{2}$
(b) $\dfrac{1}{2}$
(c) $1$
(d) $2$
Step-by-Step Solution
Key Concept: $\sin \theta = \cos \theta \Rightarrow \theta = 45^\circ$. $2(1)^2 + (1/\sqrt{2})^2 - 1 = 2 + 1/2 - 1 = 3/2$.
$\theta = 45^\circ \Rightarrow 2(1) + 1/2 - 1 = 3/2$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating expression $= 3/2$: 1.0 Mark
Correct Answer: $\dfrac{3}{2}$
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