Q. If $\theta = \tan^{- 1}{a,\phi}$ =$\tan^{- 1}{b\ }and\ ab$=$- 1,$then ($\theta - \phi)$ is equal to
A) 0
B) $\frac{\pi}{4}$
C) $\frac{\pi}{2}$
D) None of these
Explanation
(c)
Given that, $\theta = \tan^{- 1}a\ and\ \phi = \tan^{- 1}b$
And $ab = - 1$
$\therefore\tan{\theta\tan\phi} = ab = - 1$
$\Rightarrow \tan{\theta = - \cot\phi}$
$\Rightarrow \tan{\theta = \tan\left( \frac{\pi}{2} + \phi \right)}$
$\Rightarrow \theta - \phi$= $\frac{\pi}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.