How do I verify this equation is an identity? cos(x+y)/cosx cosy=1-tanx tany

1 Answer
Jim G.
Mar 18, 2018

#"see explanation"#

Explanation:

#"using the "color(blue)"trigonometric identity"#

#•color(white)(x)cos(x+y)=cosxcosy-sinxsiny#

#"consider the left side"#

#(cos(x+y))/(cosxcosy)#

#=(cosxcosy-sinxsiny)/(cosxcosy)#

#=cancel(cosxcosy)/cancel(cosxcosy)-(sinxsiny)/(cosxcosy)#

#=1-(sinx/cosx xxsiny/cosy)#

#=1-tanxtany=" right side "rArr"verified"#

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