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1.
$\sin^2\alpha+\cos^2\alpha=1$
Trigonometry
2.
$\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}$
Trigonometry
3.
$\cot\alpha=\dfrac{\cos\alpha}{\sin\alpha}$
Trigonometry
4.
$\tan\alpha\cdot\cot\alpha=1$
Trigonometry
5.
$\tan^2\alpha=\dfrac{1}{\cos^2\alpha}-1$
Trigonometry
6.
Sine of sum of angles
$\sin(\alpha+\beta)=\sin\alpha \, \cos\beta + \sin\beta \, \cos\alpha$
Trigonometry
7.
$\sin(\alpha - \beta) = \sin\alpha \, \cos\beta - \sin\beta\,\cos\alpha$
Trigonometry
8.
$\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta$
Trigonometry
9.
$\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta$
Trigonometry
10.
$\tan(\alpha+\beta)=\dfrac{\tan\alpha + \tan\beta}{1-\tan\alpha\tan\beta}$
Trigonometry
11.
$\tan(\alpha-\beta)=\dfrac{\tan\alpha - \tan\beta}{1+\tan\alpha\tan\beta}$
Trigonometry
12.
$\cot(\alpha+\beta)=\dfrac{1-\tan\alpha\tan\beta}{\tan\alpha+\tan\beta}$
Trigonometry
13.
$\cot(\alpha-\beta)=\dfrac{1+\tan\alpha\tan\beta}{\tan\alpha-\tan\beta}$
Trigonometry
14.
$\sin\left(2\alpha\right)=2\sin\alpha \cos\alpha$
Double angle
Trigonometry
15.
$\cos\left(2\alpha\right)=\cos^2\alpha - \sin^2\alpha$
Double angle
Trigonometry
16.
$\tan\left(2\alpha\right)=\dfrac{2\tan\alpha}{1+\tan^2\alpha}$
Double angle
Trigonometry
17.
$\tan\left(2\alpha\right)=\dfrac{2}{\cot\alpha-\tan\alpha}$
Double angle
Trigonometry
18.
$\cot\left(2\alpha\right)=\dfrac{\cot^2\alpha-1}{2\cot\alpha}$
Double angle
Trigonometry
19.
$\cot\left(2\alpha\right)=\dfrac{\cot\alpha-\tan\alpha}{2}$
Double angle
Trigonometry
20.
Half Angle Formula of Sine
$\sin \dfrac{\alpha}{2} = \pm \sqrt{\dfrac{1-\cos\alpha}{2}}$
Half angle
Trigonometry

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