How do you prove $(1+tan x) / (1+cot x) = 2$ ?

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Answer 1 · 2015-07-11T21:08:31

Let's suppose we were to even go through with this.

$(1+tanx)/(1+(1/tanx))*(tanx)/(tanx)$

$= (tanx+tan^2x)/(tanx+1)$

$= tanx/(tanx+1) + tan^2x/(tanx+1)$

$= (tanx+1)/(tanx+1) - cancel(1/(tanx+1)) + (tan^2x - 1)/(tanx+1) + cancel(1/(tanx+1))$

$= (tanx+1)/(tanx+1) + (tan^2x - 1)/(tanx+1)$

$= 1 + ((tanx - 1)cancel((tanx+1)))/cancel((tanx+1))$

$= 1 + tanx - 1$

$= color(blue)(tanx)$

So clearly, this is not true. This is equal to $tanx$ .

How do you prove (1+tan x) / (1+cot x) = 2(1+tan x) / (1+cot x) = 2?