Question

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

• A. $\theta =\frac{n\pi }{7}+\frac{\pi }{14}$
• B. $\theta =\frac{n\pi }{7}+\frac{\pi }{5}$
• C. $\theta =\frac{n\pi }{7}+\frac{\pi }{2}$
• D. $\theta =\frac{n\pi }{7}+\frac{\pi }{3}$

Answer 1

Answer: (A)

We have $\tan 5\theta =\cot 2\theta$
$\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]$
$\Rightarrow 5\theta =n\pi +\frac{\pi }{2}-2\theta$
$\Rightarrow 7\theta =n\pi +\frac{\pi }{2}$
$\Rightarrow \theta =\frac{n\pi }{7}+\frac{\pi }{14}$