Question

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

• A. $x=\frac{n\pi }{7}+\frac{\pi }{2},n\in Z$
• B. $x=\frac{n\pi }{7}-\frac{\pi }{14},n\in Z$
• C. $x=\frac{n\pi }{7}+\frac{\pi }{14},n\in Z$
• D. $x=\frac{n\pi }{7}+\frac{\pi }{3},n\in Z$

Answer 1

The correct option is C $x=\frac{n\pi }{7}+\frac{\pi }{14},n\in Z$

$\tan 5x=\cot 2x$

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

We know the general solution of $\tan x=\tan \alpha$ is $x=n\pi +\alpha ,n\in Z$

So,
$5x=n\pi +(\frac{\pi }{2}-2x)$

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

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

Hence, the option (C) is correct.