1.5.4—Trig identities

Identities such as sin²x+cos²x=1, tanx=sinx/cosx and 1+tan²x=sec²x follow from definitions and hold wherever both sides are defined.

To prove an identity, simplify one side to the other using a common denominator or a fundamental identity; do not assume the result you are trying to prove.

(1−cos²x)/sinx simplifies to sinx when sinx≠0 because 1−cos²x=sin²x.

Algebraic cancellation can remove values where a denominator is zero; record the excluded angles even if the simplified expression looks defined.