# Sum of Squares of Sine and Cosine/Proof 4

$\cos^2 x + \sin^2 x = 1$
 $\displaystyle \cos^2 x + \sin^2 x$ $=$ $\displaystyle \left({\cos x + i \, \sin x}\right) \, \left({\cos x - i \, \sin x}\right)$ factoring over the complex numbers $\displaystyle$ $=$ $\displaystyle \left({\cos x + i \, \sin x}\right) \, \left({\cos \left({-x}\right) + i \, \sin \left({-x}\right)}\right)$ Cosine Function is Even and Sine Function is Odd $\displaystyle$ $=$ $\displaystyle e^{ix} \, e^{-ix}$ Euler's Formula $\displaystyle$ $=$ $\displaystyle 1$
$\blacksquare$