How do you simplify #sin(x+y)-cos(x-y)# to trigonometric functions of x and y?

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Answer 1 · 2016-02-29T00:18:57

It is

#sin(x+y)-cos(x-y)=sinx*cosy+cosx*siny-cosx*cosy-sinx*siny= cosx(siny-cosy)+sinx(cosy-siny)=(cosx-sinx)(siny-cosy)#

Answer 2 · 2016-02-29T01:30:43

= (sin x + cos x)(cos y - sin y)

S = sin x.cos y + sin y.cos x - cos x.cos y - sin x.sin y.
S = sin x(cos y - sin y) - cos x(cos y - sin y) =
S = (sin x + cos x)(cos y - sin y)