3-tan-x-cot-x-3-tan-x-cot-x-1-0-

Question Number 135419 by liberty last updated on 13/Mar/21

\sqrt{3} \tan x . \cot x + \sqrt{3} \tan x - \cot x - 1 = 0

Answered by benjo_mathlover last updated on 13/Mar/21

\Rightarrow \sqrt{3} \tan x (\cot x + 1) - (\cot x + 1) = 0

(\sqrt{3} \tan x - 1) (\cot x + 1) = 0

{\begin{cases} \tan x = \frac{1}{\sqrt{3}} \\ \cot x = - 1 \Rightarrow \tan x = - 1 \end{cases}

{\begin{cases} x = \frac{π}{6} + n π \\ x = \frac{3 π}{4} + n π \end{cases}