Inverse Trigonometric Functions Question 131
Question: If $ \theta ={{\tan }^{-1}}a,\varphi ={{\tan }^{-1}}b $ and $ ab=-1, $ then $ \theta -\varphi = $
Options:
A) 0
B) $ \frac{\pi }{4} $
C) $ \frac{\pi }{2} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Given that $ \theta ={{\tan }^{-1}}a $ and $ \varphi ={{\tan }^{-1}}b $ and $ ab=-1 $ .
$ \Rightarrow \tan \theta \tan \varphi =-1\Rightarrow \tan \theta =-\cot \varphi $
$ \Rightarrow \theta -\varphi =\frac{\pi }{2} $ .
BETA
