Question

Find the general solution of $2\tan x-\cot x+1=0$

Answer 1

$2\tan x-\cot x+1=0$

$2\tan x-1/\tan x+1=0$

$2{\tan }^{2}x-1+\tan x=0$

$2{\tan }^{2}x+\tan x-1=0$

$2{\tan }^{2}x+2\tan x-\tan x-1=0$

$2\tan x(\tan x+1)-1(\tan x+1)=0$

$(\tan x+1)(2\tan x-1)=0$

$\tan x+1=0or2\tan x-1=0$

$\tan x=-1or\tan x=1/2$

$x=3\pi /4,7\pi /4$