Question

If $\theta =ta{n}^{-1}a,\varphi =ta{n}^{-1}bandab=-1,then\theta -\varphi =$

• A. \N
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. None of these

Answer 1

The correct option is C $\frac{\pi }{2}$

Given that$\theta =ta{n}^{-1}aand\varphi ta{n}^{-1}bandab=-1\Rightarrow tan\theta tan\varphi =-1\Rightarrow tan\theta =-cot\varphi \Rightarrow \theta -\varphi =\frac{\pi }{2}.$