Mathematics - Trigonometric Equation Question with Solution | TestHub

We have $\tan 5\theta =\cot 2\theta$
$\begin{array}{rl}& \Rightarrow \tan 5\theta =\tan \left(\frac{\pi }{2}-2\theta \right)\dots \\ & \left[\because \tan \left(\frac{\pi }{2}-\theta \right)=\cot \theta \right]\\ & \Rightarrow 5\theta =n\pi +\frac{\pi }{2}-2\theta \Rightarrow 7\theta =n\pi +\frac{\pi }{2}\\ & \Rightarrow \theta =\frac{n\pi }{7}+\frac{\pi }{14}.\end{array}$