Trigonometry: is there intuitive proof of $\sin(x + y)= \sin x\cos y+ \sin y\cos x$ when $x + y > 90^\circ$? I saw nice geometric proof of $\sin{(x + y)} = \sin{x}\cos{y} + \sin{y}\cos{x}$ using unit circle. But I can't find proof when $x + y > 90^\circ.$ 
Is there intuitive, "simple" or geometric way to prove this? Can we maybe transform unit circle or what is going on here? 

Let $x$ and $y$ be any argument angles in the Argand diagram. Then,
$ e^{i (x+y)} = e^{i x } e^{i y }$,
or 
$$\cos (x+y)+ i\sin(x+y) =(\cos x+i \sin x)(\cos y+i \sin y)$$
Match the real and imaginary parts to obtain
$$\cos(x+y)=\cos x\cos y-\sin x\sin y$$
$$\sin(x+y)=\sin x\cos y+\cos x\sin y$$
