If x+ y= y- x , where 0 < y < x < (π)/(2) , then what is...

\sin x+\sin y=\cos y-\cos x\frac{\sin x+\sin y}{\cos y-\cos x}=1\frac{2 \sin \left(\frac{x+y}{2}\right) \cdot \cos \left(\frac{x-y}{2}\right)}{2 \sin \left(\frac{x+y}{2}\right) \cdot \sin \left(\frac{x-y}{2}\right)}=1\cot \left(\frac{x-y}{2}\right)=1 \Rightarrow \tan \left(\frac{x-y}{2}\right)=1