$$\cos{w}=\frac{e^{iw}+e^{-iw}}{2} \enspace\land\enspace i\sin{w}=\frac{e^{iw}-e^{-iw}}{2} \enspace\land\enspace \textrm{the Euler Identity} \enspace\Rightarrow\enspace e^{iw}=\cos{w}+i\sin{w} \enspace\therefore\enspace \cos{w}=\frac{\cos{w}+i\sin{w}+\cos{w}+i\sin{w}}{2} \enspace\land\enspace i\sin{w}=\frac{\cos{w}+i\sin{w}-\cos{w}+i\sin{w}}{2}$$