Question #21fcb

1 Answer
ProfLayton
Jan 11, 2018

Proof below

Explanation:

We first use the cosine sum expansions:
#cos(x-y)/cos(x+y)=cosxcosy+sinxsiny/cosxcosy-sinxsiny#
Then divide top and bottom by #cosxcosy#
#=((cosxcosy+sinxsiny)/(cosxcosy))/((cosxcosy-sinxsiny)/(cosxcosy))#
And simplify
#=(1+tanxtany)/(1-tanxtany)#

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