Inverse Trigonometric Functions Question 173
Question: The solution set of the equation $ {{\sin }^{-1}}x=2{{\tan }^{-1}}x $ is
[AMU 2002]
Options:
A) {1, 2}
B) {-1, 2}
C) {-1, 1, 0}
D) {1, 1/2, 0}
Show Answer
Answer:
Correct Answer: C
Solution:
$ {{\sin }^{-1}}x=2{{\tan }^{-1}}x $
Therefore $ {{\sin }^{-1}}x={{\sin }^{-1}}\frac{2x}{1+x^{2}} $
$ \Rightarrow \frac{2x}{1+x^{2}}=x $
Therefore $ x^{3}-x=0 $
Therefore $ x(x+1)(x-1)=0 $
Therefore $ x={ -1,1,0 } $ .
BETA
