Compound angle identities

Compound angle identities are trigonometric identities that allow you to simplify expressions involving the sum or difference of two angles. Some of the most commonly used compound angle identities are:

• sin(θ + φ) = sin(θ)cos(φ) + cos(θ)sin(φ)
• sin(θ – φ) = sin(θ)cos(φ) – cos(θ)sin(φ)
• cos(θ + φ) = cos(θ)cos(φ) – sin(θ)sin(φ)
• cos(θ – φ) = cos(θ)cos(φ) + sin(θ)sin(φ)

These identities can be used to find the sine and cosine of the sum or difference of two angles, and they are useful for solving problems involving complex trigonometry. They are based on the definitions of the sine and cosine functions and the addition formula for the sine and cosine.