Inverse Trigonometric Functions Question 77
Question: The equation $ {{\sin }^{-1}}(3x-4x^{3})=3si{n^{-1}}(x) $ is true for all values of x lying in which one of the following intervals?
Options:
A) $ [ -\frac{1}{2},\frac{1}{2} ] $
B) $ [ \frac{1}{2},1 ] $
C) $ [ -1,-\frac{1}{2} ] $
D) $ [-1,1] $
Show Answer
Answer:
Correct Answer: D
Let $ {{\sin }^{-1}}x=\theta \Rightarrow x=\sin \theta $
$ {{\sin }^{-1}}(3sin\theta -4sin^{3}\theta )=si{n^{-1}}\sin 3\theta $
$ =3\theta =3{{\sin }^{-1}}x $
Equation $ {{\sin }^{-1}}(3x-4x^{3})=3si{n^{-1}}x $ is true for all values of x lying the interval [-1, 1].
BETA
