Identity library · 3 formulas
Pythagorean identities
The three Pythagorean identities come from one equation: divide sin²θ + cos²θ = 1 by sin²θ or by cos²θ and you get 1 + tan²θ = sec²θ and 1 + cot²θ = csc²θ. Reach for them when a squared term has to disappear, when a 1 + (something)² shows up under a radical, or when you need to trade between sin/cos and tan/sec.
Every pythagorean identities on this site
| Formula | Name | Used for |
|---|---|---|
| sin²θ + cos²θ = 1 | Pythagorean identity | simplify, verify, solve |
| 1 + tan²θ = sec²θ | Pythagorean identity (tangent form) | simplify, verify, integrate |
| 1 + cot²θ = csc²θ | Pythagorean identity (cotangent form) | simplify, verify, integrate |
Pythagorean identities (3)
sin²θ + cos²θ = 1 and the two versions you get by dividing it.
| Identity | Name | proof |
|---|---|---|
| sin²θ + cos²θ = 1 | Pythagorean identity | proof |
| 1 + tan²θ = sec²θ | Pythagorean identity (tangent form) | proof |
| 1 + cot²θ = csc²θ | Pythagorean identity (cotangent form) | proof |
Doing something with them
- Which identity should I use? — describe an expression, get the rule.
- Verify — check a claim, see a counterexample if it is false.
- Printable cheat sheet — this family pre-selected.