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