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Prove that $\frac{\sin x-\sin y}{\cos x+\cos y}=\tan \frac{x-y}{2}$
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L.H.S. $=\frac{\sin x-\sin y}{\cos x+\cos y}=\frac{2 \cos \frac{x+y}{2} \sin \frac{x-y}{2}}{2 \cos \frac{x+y}{2} \cos \frac{x-y}{2}}$
$=\frac{\sin \frac{x-y}{2}}{\cos \frac{x-y}{2}}=\tan \frac{x-y}{2}=$ R.H.S.
$=\frac{\sin \frac{x-y}{2}}{\cos \frac{x-y}{2}}=\tan \frac{x-y}{2}=$ R.H.S.
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