Introduction to Trigonometry
RD Sharma
CBSE
Grade 10
Question:
If $\sin \theta + \cos \theta = \sqrt{2} \cos \theta$, then $\tan \theta$ is equal to:
(a) $\sqrt{2} - 1$
(b) $\sqrt{2} + 1$
(c) $\dfrac{1}{\sqrt{2}}$
(d) $\sqrt{3}$
Step-by-Step Solution
Key Concept: Divide both sides by $\cos \theta$: $\tan \theta + 1 = \sqrt{2} \Rightarrow \tan \theta = \sqrt{2} - 1$.
$\tan \theta + 1 = \sqrt{2} \Rightarrow \tan \theta = \sqrt{2} - 1$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Solving $\tan \theta = \sqrt{2} - 1$: 1.0 Mark
Correct Answer: $\sqrt{2} - 1$
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