Trigonometry: Compound and Double Angles
Gr 12

The Grade 12 Trigonometry: Compound and Double Angles module extends learners’ understanding of trigonometric identities by introducing the compound-angle and double-angle formulas used to simplify expressions and solve more advanced trigonometric problems. This chapter develops strong algebraic manipulation skills and prepares students for university-level trigonometry and calculus.

Learners explore the compound-angle identities for
sin⁡(A±B)\sin(A \pm B)sin(A±B),
cos⁡(A±B)\cos(A \pm B)cos(A±B), and
tan⁡(A±B)\tan(A \pm B)tan(A±B),
as well as the double-angle identities for sine, cosine, and tangent. The lessons guide students through applying these identities to simplify complex expressions, prove trigonometric statements, and solve equations involving compound or doubled angles. Emphasis is placed on selecting appropriate identities, recognising patterns, and presenting solutions using clear mathematical reasoning.

By the end of this module, learners will be able to use compound-angle and double-angle identities confidently, transform and simplify trigonometric expressions, and solve advanced trigonometric equations—providing a strong foundation for Grade 12 examinations and for further mathematical studies requiring advanced trigonometric techniques.