Inverse Trigonometric Functions
NCERT Class 12
CBSE
Grade 12
Question:
Find the value of $\sin(\tan^{-1} x)$, $|x| < 1$.
Step-by-Step Solution
Let $\theta = \tan^{-1} x \Rightarrow \tan \theta = x$. [1.0 Mark]
$\sin(\tan^{-1} x) = \sin \theta = \dfrac{x}{\sqrt{1 + x^2}}$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Setting up right triangle with $\tan\theta = x$: 1.0 Mark
Evaluating $\sin\theta = x/\sqrt{1+x^2}$: 1.0 Mark
Correct Answer:
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