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Question: Answered & Verified by Expert
The solution set of the equation $\sin ^{-1} x=2 \tan ^{-1} x$ is
MathematicsInverse Trigonometric FunctionsJEE Main
Options:
  • A $\{1,2\}$
  • B $\{-1,2\}$
  • C $\{-1,1,0\}$
  • D $\{1,1 / 2,0\}$
Solution:
1193 Upvotes Verified Answer
The correct answer is: $\{-1,1,0\}$
$\begin{array}{ll}\sin ^{-1} x=2 \tan ^{-1} x \Rightarrow \sin ^{-1} x=\sin ^{-1} \frac{2 x}{1+x^2} \\ \Rightarrow \frac{2 x}{1+x^2}=x \Rightarrow x^3-x=0 \\ \Rightarrow x(x+1)(x-1)=0 \Rightarrow x=\{-1,1,0\}\end{array}$

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