IB Maths AA AHL 3.10 - Compound Angle Identities

This IB Maths AA AHL Topic 3.10 – Compound Angle Identities resource develops students’ understanding of compound-angle and double-angle identities for sine, cosine, and tangent. It begins by introducing the identities for sin(A + B), sin(A - B), cos(A + B), cos(A - B), tan(A + B), and tan(A - B). Students then use familiar exact values to calculate trigonometric values for less familiar angles, including sin(75°), cos(15°), and tan(75°).

The lesson also shows how the double-angle identities for sin(2x), cos(2x), and tan(2x) can be derived from the compound-angle formulas. Students practise finding exact values from given trigonometric ratios, applying quadrant information, rationalising denominators, and selecting the correct identity for expressions involving two different angles. The resource concludes by connecting the double-angle identities to De Moivre’s Theorem, giving advanced students insight into the wider mathematical structure behind the formulas. With clear identity summaries, worked derivations, exact-value problems, quadrant reasoning, exam tips, and fully worked solutions, this resource helps AHL students build strong algebraic and trigonometric fluency in line with IB Mathematics AA expectations.