Answer
$\dfrac {\sin \left( x+y\right) }{\cos \left( x-y\right) }=\dfrac {\cot y+\cot x}{1+\cot y\cot x}$
Work Step by Step
$\dfrac {\sin \left( x+y\right) }{\cos \left( x-y\right) }=\dfrac {\sin x\cos y+\cos x\sin y}{\cos x\cos y+\sin x\sin y}=\dfrac {\dfrac {\sin x\cos y+\cos x\sin y}{\sin x\sin y}}{\dfrac {\cos x\cos y+\sin x\sin y}{\sin x\sin y}}=\dfrac {\cot y+\cot x}{1+\cot y\cot x}$
