Inverse Trigonometric Functions Question 109
Question: Let $ -1\le x\le 1. $ If $ \cos (si{n^{-1}}x)=\frac{1}{2}, $ then how many value does $ \tan (co{s^{-1}}x) $ assume?
Options:
A) One
B) Two
C) Four
D) Infinite
Show Answer
Answer:
Correct Answer: B
As given : $ \cos ( {{\sin }^{-1}}x )=\frac{1}{2} $
$ \Rightarrow {{\sin }^{-1}}x={{\cos }^{-1}}( \frac{1}{2} ) $
$ \Rightarrow x=\sin \frac{\pi }{3}=\frac{\sqrt{3}}{2} $
$ \therefore \tan (co{s^{-1}}x)=tan( {{\cos }^{-1}}\frac{\sqrt{3}}{2} ) $
$ =\tan ( \pm \frac{\pi }{6} )=\pm \frac{1}{\sqrt{3}} $ Hence, $ \tan (co{s^{-1}}x) $ have two values.
BETA
