Sum and Difference Formulas for Trigonometric Functions

In trigonometry, sum and difference formulas are useful for simplifying expressions and solving equations involving angles. These formulas allow us to express the sine, cosine, and tangent of a sum or difference of two angles in terms of the sine, cosine, and tangent of the individual angles.

Sum and Difference Formulas


Applications of Sum and Difference Formulas

  1. Finding Exact Values – Using these formulas, we can compute the trigonometric values of angles that are sums or differences of special angles. For example:
Using the sum formula:
  1. Proving Identities – Many trigonometric identities are derived using sum and difference formulas.
  2. Solving Trigonometric Equations – The formulas allow for solving equations involving sums and differences of angles.
  3. Physics and Engineering Applications – These formulas are used in wave interference, signal processing, and oscillations.