Question

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

 

Answer 1

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