These are derived from the additional formulae.

$\sin{2A} ≡ 2\sin{A}\cos{A}$

$\cos{2A} ≡ \cos^2{A} - \sin^2{A}$

$\cos{2A} ≡ 1 - 2\sin^2{A}$

$\cos{2A} ≡ 2\cos^2{A} - 1$

$\tan{2A} ≡ \dfrac{2\tan{A}}{1 - \tan^2{A}}$