Inverse Trigonometric Functions Question 141
Question: If $ {{\cos }^{-1}}( \frac{1}{x} )=\theta $ , then $ \tan \theta $ =
[MNR 1978; MP PET 1989]
Options:
A) $ \frac{1}{\sqrt{x^{2}-1}} $
B) $ \sqrt{x^{2}+1} $
C) $ \sqrt{1-x^{2}} $
D) $ \sqrt{x^{2}-1} $
Show Answer
Answer:
Correct Answer: D
Solution:
Given that $ {{\cos }^{-1}}( \frac{1}{x} )=\theta \Rightarrow \cos \theta =\frac{1}{x} $ Now, $ \tan \theta =\frac{\sin \theta }{\cos \theta }=\frac{\sqrt{1-{{(1/x)}^{2}}}}{1/x}=\sqrt{x^{2}-1} $
BETA
