25.5.3 Double-Angle Formulas
Core ideaReplace β with α and the sum formulas instantly become the 'one angle doubled' forms sin2α, cos2α, and tan2α.
Module goal. We build the rules for combining known angles into new ones — starting from the sum and difference formulas to reach double-angle and auxiliary-angle forms — so messy trig expressions can be simplified, combined, and evaluated.