Inverse Trigonometric Functions Question 158
Question: $ {{\tan }^{-1}}\frac{1}{\sqrt{x^{2}-1}}= $
Options:
A) $ \frac{\pi }{2}+cose{c^{-1}}x $
B) $ \frac{\pi }{2}+{{\sec }^{-1}}x $
C) $ cose{c^{-1}}x $
D) $ {{\sec }^{-1}}x $
Show Answer
Answer:
Correct Answer: C
Solution:
$ {{\tan }^{-1}}\frac{1}{\sqrt{x^{2}-1}}={{\tan }^{-1}}\frac{1}{\sqrt{cose{c^{2}}\theta -1}} $ (Putting $ x=cosec\theta ) $
$ ={{\tan }^{-1}}\frac{1}{\cot \theta }=\theta =cose{c^{-1}}x $ .
BETA
