Prove that $cosycos(x-y)-sinysin(x-y)=cosx$ ?

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Answer 1 · 2016-12-03T07:15:52

Please see below.

Recall the identity $cos(A+B)=cosAcosB-sinAsinB$

Putting $A=y$ and $B=x-y$ , we get $A+B=y+x-y=x$ and the above identity becomes

$cosycos(x-y)-sinysin(x-y)=cosx$

Prove that cosycos(x-y)-sinysin(x-y)=cosxcosycos(x-y)-sinysin(x-y)=cosx?