# Find the General Solution of the Following Equation: Tan 3 X = Cot X - Mathematics

Sum

Find the general solution of the following equation:

$\tan 3x = \cot x$

#### Solution

We have:

$\tan3x = \cot x$

$\Rightarrow \tan3x = \tan \left( \frac{\pi}{2} - x \right)$

$\Rightarrow 3x = n\pi + \left( \frac{\pi}{2} - x \right), n \in Z$

$\Rightarrow 4x = n\pi + \frac{\pi}{2}, n \in Z$

$\Rightarrow x = \frac{n\pi}{4} + \frac{\pi}{8}, n \in Z$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 2.06 | Page 21