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tex]\displaystyle{\sin(A\pm B)=\sin A\cos B\pm\cos A\sin B}[/tex]
tex]\displaystyle{\cos(A\pm B)=\cos A\cos B\mp\sin A\sin B}[/tex]
tex]\displaystyle{\tan(A\pm B)=\frac{\tan A\pm\tan B}{1\mp\tan A\tan B}}[/tex]
tex]\displaystyle{\sin 3A=3\sin A-4\sin^{3}A}[/tex]
tex]\displaystyle{\cos 3A=4\cos^{3}A-3\cos A}[/tex]
tex]\displaystyle{\tan 3A=\frac{3\tan A-\tan^{3}A}{1-3\tan^{2}A}}[/tex]
tex]\displaystyle{\sin\left(\frac{A}{2}\right)=\sqrt{\frac{1-\cos A}{2}}}[/tex]
tex]\displaystyle{\cos\left(\frac{A}{2}\right)=\sqrt{\frac{1+\cos A}{2}}}[/tex]
tex]\displaystyle{\tan\left(\frac{A}{2}\right)=\sqrt{\frac{1-\cos A}{1+\cos A}}}[/tex]
tex]\displaystyle{\sin A\pm\sin B=2\sin\left(\frac{A\pm B}{2}\right)\cos\left(\frac{A\mp B}{2}\right)}[/tex]
tex]\displaystyle{\cos A\pm\cos B=(1\pm 1)\cos\left(\frac{A\pm B}{2}\right)\cos\left(\frac{A\mp B}{2}\right)+(1\mp 1)\sin\left(\frac{A\pm B}{2}\right)\sin\left(\frac{A\mp B}{2}\right)}[/tex]
tex]\displaystyle{\frac{\displaystyle{\sum_{k=1}^{n}\sin k\theta}}{\displaystyle{\sum_{k=1}^{n}\cos k\theta}}=\tan\frac{(n+1)\theta}{2}}}[/tex]