Edexcel A-Level Maths: Trigonometric Identities

A set of vocabulary flashcards reviewing the essential trigonometric identities and double-angle formulas for Edexcel A-Level Mathematics.

Pythagorean identity

$$\sin^2(\theta) + \cos^2(\theta) = 1$$

Secant identity

$$\sec^2(\theta) = 1 + \tan^2(\theta)$$

Cosecant identity

$$\operatorname{cosec}^2(\theta) = 1 + \cot^2(\theta)$$

Double-angle sine

$$\sin(2\theta) = 2\sin(\theta)\cos(\theta)$$

Double-angle cosine (in terms of $\cos(\theta)$ and $\sin(\theta)$)

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

Double-angle cosine (in terms of $\sin(\theta)$)

$$\cos(2\theta) = 1 - 2\sin^2(\theta)$$

Double-angle cosine (in terms of $\cos(\theta)$)

$$\cos(2\theta) = 2\cos^2(\theta) - 1$$

Double-angle tangent

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