Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Solve the Following Equation: Cot X + Tan X = 2 - Mathematics

Sum

Solve the following equation:
$\cot x + \tan x = 2$

#### Solution

$\cot x + \tan x = 2$
$\Rightarrow \frac{1}{\tan x} + \tan x = 2$
$\Rightarrow \tan^2 x + 1 = 2\tan x$
$\Rightarrow \tan^2 x - 2\tan x + 1 = 0$
$\Rightarrow \left( \tan x - 1 \right)^2 = 0$
$\Rightarrow \tan x = 1 = \tan\frac{\pi}{4}$
$\Rightarrow x = n\pi + \frac{\pi}{4}, n \in Z \left( \tan\theta = \tan\alpha \Rightarrow \theta = n\pi + \alpha, n \in Z \right)$
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 7.1 | Page 22