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 } $
Show Answer
Answer:
Correct Answer: C
$ {{\sin }^{-1}}x=2{{\tan }^{-1}}\sqrt{\frac{x}{2}} $
$ \Rightarrow {{\sin }^{-1}}x={{\sin }^{-1}}\left{\frac{2x}{1+x^{2}}\right} $
$ \Rightarrow 2x/(1+x^{2})=x $
$ \Rightarrow x(x+1)(x-1)=0\Rightarrow x={-1,0,1} $
BETA
