Trig Identities Calculator

What Are Trig Identities?

Trigonometric identities are equations that relate trig functions for all valid angle values. They are essential for simplifying expressions, solving equations, and finding exact values of special angles.

Related: Sum Difference Identities Calculator, Double Angle Formula Calculator, Half Angle Calculator.

Pythagorean Identity

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

Double Angle Identities

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

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

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

Composite Angle Identities

$$\sin(\alpha \pm \beta) = \sin\alpha\cos\beta \pm \cos\alpha\sin\beta$$

$$\cos(\alpha \pm \beta) = \cos\alpha\cos\beta \mp \sin\alpha\sin\beta$$