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

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