Question

The general value of $\theta$ satisfying the equation $\tan \theta+\tan \left(\frac{\pi}{2}-\theta\right) \frac{- b \pm \sqrt{ b ^{2}-4 ac }}{2 a }=2$, is

• A. $n \pi \pm \frac{\pi}{4}$
• B. $n \pi+\frac{\pi}{4}$
• C. $2 n \pi \pm \frac{\pi}{4}$
• D. $n \pi+(-1)^{ n } \frac{\pi}{4}$

Answer 1

Answer: (B)

$\tan\, \theta+\tan \left(\frac{\pi}{2}-\theta\right)=2 $
$ \Rightarrow \tan \,\theta+\frac{1}{\tan \,\theta}=2$
$\Rightarrow \tan ^{2}\, \theta-2 \tan \,\theta+1=0$
$\Rightarrow \tan\, \theta=1=\tan \frac{\pi}{4} $
$ \Rightarrow \theta= n \pi+\frac{\pi}{4}$