Question

Prove (1+tanx)/(1+cotx)=tanx by algebra

Answer 1

`\text{L.H.S}\\\\=(1+\tan x)/( 1+ \cot x)\\\\\\=\frac{1+ \tan x}{ 1+ \tfrac 1{\tan x}}\\\\\\=\frac{1+\tan x}{\tfrac{\tan x+1}{\tan x}}\\\\\\=(1+\tan x) * (\tan x)/(1+ \tan x)\\\\=\tan x\\\\=\text{R.H.S}\\\\\text{Proved.}`