Inverse Trigonometric Functions
NCERT Class 12
CBSE
Grade 12
Question:
Prove that $3 \sin^{-1} x = \sin^{-1}(3x - 4x^3)$, $x \in \left[-\dfrac{1}{2}, \dfrac{1}{2}\right]$.
Step-by-Step Solution
Let $x = \sin \theta \Rightarrow \text{RHS} = \sin^{-1}(3\sin\theta - 4\sin^3\theta) = \sin^{-1}(\sin 3\theta)$. [1.0 Mark]
$= 3\theta = 3\sin^{-1} x = \text{LHS}$. Proved! [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Substituting $x = \sin\theta$: 1.0 Mark
Simplifying $\sin^{-1}(\sin 3\theta) = 3\sin^{-1}x$: 1.0 Mark
Correct Answer:
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