Search any question & find its solution
Question:
Answered & Verified by Expert
The solution set of the equation $\sin ^{-1} x=2 \tan ^{-1} x$ is
Options:
Solution:
1193 Upvotes
Verified Answer
The correct answer is:
$\{-1,1,0\}$
$\begin{array}{ll}\sin ^{-1} x=2 \tan ^{-1} x \Rightarrow \sin ^{-1} x=\sin ^{-1} \frac{2 x}{1+x^2} \\ \Rightarrow \frac{2 x}{1+x^2}=x \Rightarrow x^3-x=0 \\ \Rightarrow x(x+1)(x-1)=0 \Rightarrow x=\{-1,1,0\}\end{array}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.