[math][br]\begin{tabular}{lll}[br]\tan \alpha=\frac{\sin \alpha}{\cos\alpha}&\;&\cot\alpha=\frac{\cos \alpha}{\sin\alpha}=\frac{1}{\tan\alpha}\\[br]\sec\alpha=\frac{1}{\cos\alpha}&\;&\csc\alpha=\frac{1}{\sin\alpha}\\[br]\sin^2\alpha+\cos^2\alpha=1&\;&\sin^2\alpha=1-\cos^2\alpha\\[br]\;&\;&\cos^2\alpha=1-\sin^2\alpha\\[br]1+\tan^2\alpha=\frac{1}{\cos^2\alpha}&\;&1+\cot^2\alpha=\frac{1}{\sin^2\alpha}[br]\end{tabular}[/math]

[math][br]\begin{tabular}{l}[br]\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta\\[br]\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta\\[br]\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta\\[br]\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta\\[br]\tan(\alpha+\beta)=\frac{\tan\alpha+tan\beta}{1-\tan\alpha\cdot\tan\beta}\\[br]\tan(\alpha-\beta)=\frac{\tan\alpha-tan\beta}{1+\tan\alpha\cdot\tan\beta}[br]\end{tabular}[br][/math]

[math][br]\begin{tabular}{ll}[br]\sin(2\alpha)=2\sin\alpha\cos\alpha & \;\\[br] \;& \;\\[br]\cos(2\alpha)=\cos^2\alpha-\sin^2\alpha & \;\\[br]\cos(2\alpha)=2\cos^2\alpha-1 & \cos^2\alpha=\frac{1+\cos2\alpha}{2}\\[br]\cos(2\alpha)=1-2\sin^2\alpha & \sin^2\alpha=\frac{1-\cos2\alpha}{2}\\[br] & \\[br]\tan 2\alpha=\frac{2\tan\alpha}{1-\tan^2\alpha} & [br]\end{tabular}[br][/math]

[math][br]\begin{tabular}{l}[br]\sin \alpha+\sin\beta=2\sin\left(\frac{\alpha+\beta}{2}\right)\cos\left(\frac{\alpha-\beta}{2}\right)\\[br]\sin \alpha-\sin\beta=2\cos\left(\frac{\alpha+\beta}{2}\right)\sin\left(\frac{\alpha-\beta}{2}\right)\\[br]\cos \alpha+\cos\beta=2\cos\left(\frac{\alpha+\beta}{2}\right)\cos\left(\frac{\alpha-\beta}{2}\right)\\[br]\cos \alpha-\cos\beta=-2\sin\left(\frac{\alpha+\beta}{2}\right)\sin\left(\frac{\alpha-\beta}{2}\right)\\[br]\end{tabular}[br][/math]