Answer
$\cos \left( x+y\right) \cos y+\sin \left( x+y\right) \sin y
=\left( \cos x\cos y-\sin x\sin y\right) \cos y+\left( \sin x\cos y+\cos x\sin y\right) \sin y =\cos x\cos ^{2}y-\sin x\sin y\cos y+\sin x\cos y\sin y+\cos x\sin ^{2}y=\cos x\left( \cos ^{2}y+\sin ^{2}y\right)
=\cos x $
Work Step by Step
$\cos \left( x+y\right) \cos y+\sin \left( x+y\right) \sin y=\left( \cos x\cos y-\sin x\sin y\right) \cos y+\left( \sin x\cos y+\cos x\sin y\right) \sin y =\cos x\cos ^{2}y-\sin x\sin y\cos y+\sin x\cos y\sin y+\cos x\sin ^{2}y=\cos x\left( \cos ^{2}y+\sin ^{2}y\right) =\cos x $
