Question

General solution of \[\tan 5 x = \cot 2 x\] is

Options

• \[\frac{n \pi}{7} + \frac{\pi}{2}, n \in Z\]

• \[x = \frac{n \pi}{7} + \frac{\pi}{3}, n \in Z\]

   

• \[x = \frac{n \pi}{7} + \frac{\pi}{14}, n \in Z\]

   

• \[x = \frac{n \pi}{7} - \frac{\pi}{14}, n \in Z\]

   

Answer 1

\[x = \frac{n \pi}{7} - \frac{\pi}{14}, n \in Z\]
Given:
\[\tan5x = \cot2x\]
\[ \Rightarrow \tan5x = \tan \left( \frac{\pi}{2} - 2x \right)\]
\[ \Rightarrow 5x = n\pi + \frac{\pi}{2} - 2x\]
\[ \Rightarrow 7x = n\pi + \frac{\pi}{2}\]
\[ \Rightarrow x = \frac{n\pi}{7} + \frac{\pi}{14} , n \in Z\]