25.5.5 The Auxiliary-Angle Formula: Two into One
Core ideaasinx+bcosx looks like two waves, but it can be merged into a single Rsin(x+φ) — one angle and one amplitude that say it all.
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.