Verifying identities

Math

Definition

Verifying trigonometric identities means proving that one side of a trig equation can be algebraically transformed to equal the other side. You work with only one side at a time, using known identities and algebra to make it match the other side.

How It Works

  1. Choose the more complex side to simplify (usually the left side).
  2. Convert all expressions to sine and cosine if helpful.
  3. Apply known identities (Pythagorean, reciprocal, double-angle, etc.).
  4. Simplify using algebra (factor, combine fractions, cancel) until it matches the other side.

Examples

  • Proving that sin²x + cos²x = 1 is the fundamental Pythagorean identity
  • Verifying that tan x · cos x = sin x by rewriting tan x as sin x / cos x
  • Showing that (1 − cos²x) / sin x = sin x using the Pythagorean identity

Related Terms

Pythagorean identities Double-angle formulas Sum and difference formulas Half-angle formulas

Study This Concept

Practice verifying identities with free review games in these units:

Pre-Calculus Unit 5: Analytic Trigonometry