Trigonometric Identities

High School

Definition

Trigonometric identities are equations involving trigonometric functions that hold true for all angles.

sin²θ + cos²θ = 1

Pythagorean identity

sin(A ± B) = sin A cos B ± cos A sin B

Sine addition formula

cos(A ± B) = cos A cos B ∓ sin A sin B

Cosine addition formula

sin 2θ = 2sinθcosθ

Double angle formula (sine)

cos 2θ = cos²θ - sin²θ

Double angle formula (cosine)

Example 1

Find sin 75° using special angles.