Trig Identities | Curiwise

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Hook

Equations that are always true

An identity isn't an equation to solve for x — it's a statement that's true for EVERY x. sin²θ + cos²θ = 1, for instance, holds at every angle, because it's just the Pythagorean theorem on a unit-radius circle. Identities are the algebra of trig: they let you rewrite expressions, simplify integrals, and solve equations that would otherwise be stuck. The handful you'll meet here — Pythagorean, sum/difference, double-angle — do most of the work in pre-calculus and calculus.

An identity is true for all values of the variable. It's a rewriting tool, not a solve-for-x.

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