2.3.2—Trig identities

Use compound-angle, double-angle and half-angle identities to rewrite expressions into a form suited to the question. For example, sin2x=2sinx cosx and cos2x=1−2sin²x.

Choose one direction of simplification, keep domain restrictions, and avoid replacing an identity with a numerical check at a few angles.

1−cos2x=2sin²x converts a cosine expression into a square that is easier to integrate or solve.

An identity is true for every allowed x; a relation that works only at selected angles is not an identity.