Trigonometric identities

Use sin²x + cos²x = 1 and tan x = sin x/cos x to rewrite expressions. Every denominator must be nonzero. Algebraic simplification proves equality only where both original sides are defined.

For a proof, start from one side and transform it into the other, or transform both sides to an expression already known to be equal. Squaring or multiplying by a zero-valued expression can lose information, so record restrictions.

Worked example

Simplify (1 − cos²x)/sin x, where sin x ≠ 0.

1. Replace 1 − cos²x by sin²x.
2. Cancel one factor sin x under the stated restriction.

Answer: sin x, for sin x ≠ 0

Revise first: Algebraic fractions.