satisfying the equation \[\tan \theta +\tan \left( \frac{\pi }{2}-\theta \right)=2\], is [MNR 1974]
A) \[n\pi +\frac{\pi }{4}\]
B) \[n\pi +\frac{\pi }{4}\]
C) \[2n\pi \pm \frac{\pi }{4}\]
D) \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}\]
Correct Answer: B
Solution :
\[\tan \theta +\frac{1}{\tan \theta }=2\]\[\Rightarrow \] \[{{\tan }^{2}}\theta -2\tan \theta +1=0\] \[\Rightarrow \] \[\tan \theta =1=\tan \frac{\pi }{4}\] \[\Rightarrow \] \[\theta =n\pi +\frac{\pi }{4}\].
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