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

1 Answer
Feb 15, 2017

see below

Explanation:

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