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

Sum

Find the general solution of the following equation:

\[\tan px = \cot qx\]

 

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Solution

We have:

\[\tan px = \cot qx\]

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

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

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

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

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 2.09 | Page 21
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