how to evaluate $\tan x-\cot x=2$ **Question** how to evaluate $\tan x-\cot x=2.$ Given that it lies between on $\left[\frac{-\pi} 2,\frac \pi 2 \right]$. _My Steps so far_ I converted cot into tan to devolve into $\frac{\tan^2 x-1}{\tan x}=2$. Then I multiply $\tan{x}$ on both sides and then get $\tan^2 x-2\tan x-1$. From there I dont know where to go.

We then can solve the quadratic equation thus getting $$\tan x =\frac {2 \pm \sqrt{4-4 (1)(-1)}}{2} = \frac {2\pm 2\sqrt {2}}{2} = 1\pm \sqrt {2} $$ Thus $$x =\arctan ( 1\pm \sqrt {2}) $$ Hope it helps.