# Mathematical Formulae

### Generally used:

$(a+b)^{2} = a^{2}+b^{2}+2ab$

$(a+b)^{2} = a^{2}+b^{2}-2ab$

$(a+b)^{3} = a^{3}+b^{3}+3ab^{2}+3a^{2}b$

$\frac{U}{V}=\frac{U'V-UV'}{V^2}$

$d(UV) = UV'+VU'$

$\int UVdx = UV_{1}-U'V_{2}+U^{''}V_{3}+.....$

### Trigonometric functions:

$\sin^{2}\theta+\cos^{2}\theta=1$

$\sin(-\theta)=-\sin\theta$

$\cos(-\theta)=\cos\theta$

$\sin(A+B) = \sin A \cos B + \cos A \sin B$

$\cos(A+B) = \cos A \cos B - \sin A \sin B$

$\sin(A-B) = \sin A \cos B - \cos A \sin B$

$\cos(A-B) = \cos A \cos B + \sin A \sin B$

$\cos n\pi = (-1)^{n}$

$\sin n\pi = 0$

$\sin^{2}\theta = \frac{1-\cos2\theta}{2}$

$\cos^{2}\theta = \frac{1+\cos2\theta}{2}$

$\sin2\theta = 2\sin\theta\cos\theta$

$\cos 2\theta = \cos^2 \theta - \sin^2 \theta$

$\cos^{3}\theta = \frac{\cos3\theta+3\cos\theta}{4}$

$\sin^{3}\theta = \frac{3\sin\theta-\sin3\theta}{4}$

$\sinh x = \frac{e^{x}}{2}-\frac{e^{-x}}{2}$

$\cosh x = \frac{e^{x}}{2}+\frac{e^{-x}}{2}$

$\tan^{-1}\infty = \frac{\pi}{2}$

$\tan^{-1}(-\infty) = -\frac{\pi}{2}$