Double angle formulas formulas

Expressing trigonometric functions of an angle $2x$ in terms of functions of an angle $x$.

$\sin\left(2\alpha\right)=2\sin\alpha \cos\alpha$

$\cos\left(2\alpha\right)=\cos^2\alpha - \sin^2\alpha$

$\tan\left(2\alpha\right)=\dfrac{2\tan\alpha}{1+\tan^2\alpha}$

$\tan\left(2\alpha\right)=\dfrac{2}{\cot\alpha-\tan\alpha}$

$\cot\left(2\alpha\right)=\dfrac{\cot^2\alpha-1}{2\cot\alpha}$

$\cot\left(2\alpha\right)=\dfrac{\cot\alpha-\tan\alpha}{2}$