Question

General solution of the equation $\tan 5x=\cot 5x$ is :

• A. $n\pi \pm \frac{\pi }{20},n\in Z$
• B. $\frac{n\pi }{5}+\frac{\pi }{20},n\in Z$
• C. $\frac{n\pi }{5}\pm \frac{\pi }{4},n\in Z$
• D. $\frac{n\pi }{5}\pm \frac{\pi }{20},n\in Z$

Answer 1

The correct option is D $\frac{n\pi }{5}\pm \frac{\pi }{20},n\in Z$

$\tan 5x=\cot 5x\Rightarrow \tan 5x=\frac{1}{\tan 5x}\Rightarrow {\tan }^{2}5x=1={\tan }^2\frac{\pi }{4}\Rightarrow 5x=n\pi \pm \frac{\pi }{4}\Rightarrow x=\frac{n\pi }{5}\pm \frac{\pi }{20},n\in Z$