General solution of tan 5 x=cot 2 x is
Question:

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

(a) $\frac{n \pi}{7}+\frac{\pi}{2}, n \in Z$

(b) $x=\frac{n \pi}{7}+\frac{\pi}{3}, n \in Z$

(c) $x=\frac{n \pi}{7}+\frac{\pi}{14}, n \in Z$

(d) $x=\frac{n \pi}{7}-\frac{\pi}{14}, n \in Z$

Solution:

(c) $x=\frac{n \pi}{7}+\frac{\pi}{14}, n \in Z$

Given;

$\tan 5 x=\cot 2 x$

$\Rightarrow \tan 5 x=\tan \left(\frac{\pi}{2}-2 x\right)$

$\Rightarrow 5 x=n \pi+\frac{\pi}{2}-2 x$

$\Rightarrow 7 x=\mathrm{n} \pi+\frac{\pi}{2}$

$\Rightarrow x=\frac{\mathrm{n} \pi}{7}+\frac{\pi}{14}, \mathrm{n} \in \mathrm{Z}$