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Q. General solution of $\tan 5\,\theta=\cot 2 \,\theta$ is

Trigonometric Functions

Solution:

We have $\tan 5 \,\theta=\cot 2 \,\theta$
$\Rightarrow \tan 5 \theta=\tan \left(\frac{\pi}{2}-2 \theta\right) \ldots $$\left[\because \tan \left(\frac{\pi}{2}-\theta\right)=\cot \theta\right]$
$\Rightarrow 5 \,\theta= n \pi+\frac{\pi}{2}-2 \theta $
$\Rightarrow 7 \,\theta= n \pi+\frac{\pi}{2}$
$\Rightarrow \theta=\frac{ n \pi}{7}+\frac{\pi}{14}$