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