Find the General Solution of the Following Equation: Tan P X = Cot Q X - Mathematics

Sum

Find the general solution of the following equation:

$\tan px = \cot qx$

Solution

We have:

$\tan px = \cot qx$

$\Rightarrow \tan px = \tan \left( \frac{\pi}{2} - qx \right)$

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

$\Rightarrow (p + q)x = n\pi + \frac{\pi}{2}, n \in Z$

$\Rightarrow x = \left( \frac{2n + 1}{p + q} \right)\frac{\pi}{2}, n \in Z$

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 2.09 | Page 21