How do you prove #(sin x - sin y) / (cos x + cos y) + ( cos x - cos y) / ( sin x + sin y) = 0#?

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Answer 1 · 2016-04-17T03:00:51

See below

Left Side=#((sinx-siny)(sinx +siny)+(cosx-cosy)(cosx+cosy))/((cosx+cosy)(sinx+siny))#

#=(sin^2x-sin^2y+cos^2x-cos^2y)/((cosx+cosy)(sinx+siny))#

#=((sin^2x+cos^2x)-(sin^2y+cos^2y))/((cosx+cosy)(sinx+siny))#

#=(1-1)/((cosx+cosy)(sinx+siny))#

#=0/((cosx+cosy)(sinx+siny))#

#=0#

#=#Right Side