How do you prove $cos(x+y)cosy + sin(x+y)siny = cosx$ ?

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Answer 1 · 2016-04-28T03:36:54

Please see below

Recall the trigonometrical identity

$cos(A-B)=cosAcosB+sinAsinB$

Putting $A=x+y$ and $B=y$ , we get

$cos(x+y-y)=cos(x+y)cosy+sin(x+y)siny$

or transposing LHS to RHS and vice-versa

$cos(x+y)cosy+sin(x+y)siny=cosx$

How do you prove cos(x+y)cosy + sin(x+y)siny = cosx cos(x+y)cosy + sin(x+y)siny = cosx?