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

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08-06-2022
Mathematics

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

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loneguy loneguy · Answer 1 · 2022-06-08T04:56:14+02:00

loneguy loneguy

08-06-2022

[tex]\text{L.H.S}\\\\=\dfrac{1+\tan x}{ 1+ \cot x}\\\\\\=\dfrac{1+ \tan x}{ 1+ \tfrac 1{\tan x}}\\\\\\=\dfrac{1+\tan x}{\tfrac{\tan x+1}{\tan x}}\\\\\\=(1+\tan x) \times \dfrac{\tan x}{1+ \tan x}\\\\=\tan x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]

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