25.5.1 Cosine of a Sum or Difference
Core ideaThe cosine of two angles joined together can't simply be added; you have to unpack it with cos(α±β)=cosαcosβ∓sinαsinβ.
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.