Trigonometric Products as Sums & Differences

Trigonometric products as sums & differences is part of the Further integration topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-04). This subtopic derives, from the compound-angle formulas, identities that rewrite a product of sines and cosines as a sum or difference, for example \(2\cos A\cos B = \cos(A-B) + \cos(A+B)\).

Students and teachers will cover using these product-to-sum identities to solve equations such as \(\sin 3x + \sin x = 0\) on a given interval and to integrate expressions like \(\sin 3x\cos x\) or \(\cos 5x\cos 3x\) — a key integration technique in the HSC Extension 2 course.