Trigonometric functions

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Trigonometric functions
Hyperbolic functions
Logarithm
Conics
Vector

Derivative
Integral
Series
Ordinary differential equation

Identities

$$\begin{array}{l} \sin^2 x + \cos^2 x = 1 \\[12pt] \sin(x + y) = \sin x \cos y + \cos x \sin y \\ \cos(x + y) = \cos x \cos y - \sin x \sin y \\[6pt] \sin x \cos y = \frac{\sin(x + y) + \sin(x - y)}{2} \\ \cos x \cos y = \frac{\cos(x - y) + \cos(x + y)}{2} \\ \sin x \sin y = \frac{\sin(x - y) - \sin(x + y)}{2} \\[6pt] \sin x \pm \sin y = 2 \sin\left(\frac{x \pm y}{2}\right) \cos\left(\frac{x \mp y}{2}\right) \\ \cos x + \cos y = 2 \cos\left(\frac{x + y}{2}\right) \cos\left(\frac{x - y}{2}\right) \\ \cos x - \cos y = -2 \sin\left(\frac{x + y}{2}\right) \sin\left(\frac{x - y}{2}\right) \\ \end{array}$$