Trigonometric Products as Sums & Differences

Trigonometric products as sums and differences is part of the Further integration topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-04). This subtopic derives the identities that turn products such as \(\cos A\cos B\) and \(\sin A\cos B\) into sums and differences, for example \(\cos A\cos B = \dfrac{1}{2}[\cos(A-B) + \cos(A+B)]\).

Students and teachers will cover how to use these product-to-sum identities to solve trigonometric equations and to evaluate integrals of the form \(\displaystyle\int \sin(mx)\cos(nx)\,dx\) — a key integration technique in the HSC Extension 2 course.