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#.