The 11 Most Beautiful Mathematical Equations

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9. The relation it comes from

e^(i*x) = cos x + i sin x

is even better, since it provides a way to compute many trig identities, such as

sin^2 x + cos^2 x = (cos x + i sin x)(cos x - i sin x) = e^(i*x) * e^(-i*x) = 1

or

cos 2x = (e^(2i*x) + e^(-2i*x))/2 = (e^(i*x)^2 + e^(-i*x)^2)/2 = <-2 + (e^(i*x) + e^(-i*x))^2>/2
= -1 + 2cos^2 x = -sin^2 x - cos^2 x + 2 cos^2 x = cos^2 x - sin^2 x