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1.
$\sin\left(2\alpha\right)=2\sin\alpha \cos\alpha$
2.
$\cos\left(2\alpha\right)=\cos^2\alpha - \sin^2\alpha$
3.
$\tan\left(2\alpha\right)=\dfrac{2\tan\alpha}{1+\tan^2\alpha}$
4.
$\tan\left(2\alpha\right)=\dfrac{2}{\cot\alpha-\tan\alpha}$
5.
$\cot\left(2\alpha\right)=\dfrac{\cot^2\alpha-1}{2\cot\alpha}$
6.
$\cot\left(2\alpha\right)=\dfrac{\cot\alpha-\tan\alpha}{2}$