User DavisLiu2

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1) $\cos(x)+i\sin(x) = e^{ix}$ ~\cos(x)+i\sin(x) = e^{ix}~

2) $\cos(x)-i\sin(x) = e^{-ix}$ ~\cos(x)-i\sin(x) = e^{-ix}~

$2\cos(x) = e^{ix}+e^{-ix}$ ~2\cos(x) = e^{ix}+e^{-ix}~, $\cos(x) = \frac{e^{ix}+e^{-ix}}{2}$ ~\cos(x) = \frac{e^{ix}+e^{-ix}}{2}~

$2i\sin(x) = e^{ix}-e^{-ix}$ ~2i\sin(x) = e^{ix}-e^{-ix}~, $\sin(x) = \frac{e^{ix}-e^{-ix}}{2i}$ ~\sin(x) = \frac{e^{ix}-e^{-ix}}{2i}~