A) 0
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{2}\]
D) None of these
Correct Answer: C
Solution :
Given that \[\theta ={{\tan }^{-1}}a\] and \[\varphi ={{\tan }^{-1}}b\] and \[ab=-1\]. \[\Rightarrow \tan \theta \tan \varphi =-1\Rightarrow \tan \theta =-\cot \varphi \] \[\Rightarrow \theta -\varphi =\frac{\pi }{2}\].
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