How do you verify the identity $(sinxcosy+cosxsiny)/(cosxcosy-sinxsiny)=(tanx+tany)/(1-tanxtany)$ ?

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Answer 1 · 2017-02-15T21:27:22

see below

Right Hand Side:

$(tan x+tan y)/(1-tanxtany)=(sinx/cosx +siny/cosy)/(1-sinx/cosx siny/cosy)$

$=((sinxcosy+cosx sin y)/(cosxcosy))/(1-(sinxsiny)/(cosxcosy)$

$=((sinxcosy+cosx siny)/(cosxcosy))/((cosxcosy-sinxsiny)/(cosxcosy)$

$=(sinxcosy+cosxsiny)/(cosxcosy) *(cosxcosy)/(cosxcosy-sinxsiny)$

$=(sinxcosy+cosx sin y)/cancel(cosxcosy) *cancel(cosxcosy)/(cosxcosy-sinxsiny)$

$=(sinxcosy+cosxsiny)/(cosxcosy-sinxsiny)$

$:.=$ Left Hand Side

How do you verify the identity (sinxcosy+cosxsiny)/(cosxcosy-sinxsiny)=(tanx+tany)/(1-tanxtany)(sinxcosy+cosxsiny)/(cosxcosy-sinxsiny)=(tanx+tany)/(1-tanxtany)?