Inverse Trigonometric Functions Question 66
Question: The solutions set of the equations $ {{\sin }^{-1}}x=2{{\tan }^{-1}}x $ is
Options:
A) $ { 1,2 } $
B) $ { -1,2 } $
C) $ { -1,1,0 } $
D) $ { 1,1/2,0 } $
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Answer:
Correct Answer: C
$ {{\sin }^{-1}}x=2{{\tan }^{-1}}x $
$ \Rightarrow {{\sin }^{-1}}x={{\sin }^{-1}}{2x/(1+x^{2})} $
$ \Rightarrow 2x/(1+x^{2})=x $
$ \Rightarrow x(x+1)(x-1)=0\Rightarrow x={-1,1,0} $
BETA
