Question 843799
The shortest way is to substitute *[tex \large \cos x = \frac{e^{ix} + e^{-ix}}{2}] and *[tex \large \sin x = \frac{e^{ix} - e^{-ix}}{2i}] and prove it algebraically. See the following article:


http://mathworld.wolfram.com/TrigonometricAdditionFormulas.html