Math
Verifying identities.
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 · 4 phases
Step by step.
- Choose the more complex side to simplify (usually the left side).
- Convert all expressions to sine and cosine if helpful.
- Apply known identities (Pythagorean, reciprocal, double-angle, etc.).
- Simplify using algebra (factor, combine fractions, cancel) until it matches the other side.
Examples
Real-world.
- 1 Proving that sin²x + cos²x = 1 is the fundamental Pythagorean identity
- 2 Verifying that tan x · cos x = sin x by rewriting tan x as sin x / cos x
- 3 Showing that (1 − cos²x) / sin x = sin x using the Pythagorean identity