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Find the General Solution of the Following Equation: Tan 2 X Tan X = 1 - Mathematics

Sum

Find the general solution of the following equation:

\[\tan 2x \tan x = 1\]
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Solution

We have:

\[\tan2x \tan x = 1\]

\[\Rightarrow \tan2x = \frac{1}{\tan x}\]

\[ \Rightarrow \tan2x = \cot x\]

\[ \Rightarrow \tan2x = \tan \left( \frac{\pi}{2} - x \right)\]

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

\[ \Rightarrow 3x = n\pi + \frac{\pi}{2}, n \in Z\]

\[ \Rightarrow x = \frac{n\pi}{3} + \frac{\pi}{6}, n \in Z\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 2.07 | Page 21
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