Sum and difference formulas

Math

Definition

Trigonometric identities that express sin(A ± B), cos(A ± B), and tan(A ± B) in terms of sin, cos, and tan of A and B individually. They are essential for finding exact values of trig functions at non-standard angles.

Examples

  • sin(75°) = sin(45° + 30°) = sin45·cos30 + cos45·sin30 = (√6 + √2)/4
  • cos(15°) = cos(45° − 30°) = cos45·cos30 + sin45·sin30 = (√6 + √2)/4
Key Fact

sin(A ± B) = sinA·cosB ± cosA·sinB; cos(A ± B) = cosA·cosB ∓ sinA·sinB

Related Terms

Double-angle formulas Half-angle formulas Verifying identities Unit circle values

Study This Concept

Practice sum and difference formulas with free review games in these units:

Pre-Calculus Unit 5: Analytic Trigonometry Trigonometry Unit 5: Trigonometric Identities