How do you prove #Sin(x-y) Cos y + Cos(x-y) Sin y = Sinx#?

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Answer 1 · 2016-05-13T18:58:47

see below

Use Properties:#sin(x-y)=sinxcosy-cosxsiny# and
#cos(x-y)=cosxcosy+sinxsiny#

Left Side: #=sin(x-y)cosy+cos(x-y)siny#

#=(sinxcosy-cosxsiny)cosy+(cosxcosy+sinxsiny)siny#

#=sinxcos^2y-cosxsinycosy+cosxsinycosy+sinxsin^2y#

#=sinxcos^2y+sinxsin^2y#

#=sinx(cos^2y+sin^2y)#

#=sinx*1#

#=sinx#

#=#Right Side