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Addition (compound angle) formulae expand trigonometric functions of a sum or difference of angles — sin(A ± B), cos(A ± B) and tan(A ± B). They underpin the double angle formulae, the R-form, proving identities and solving trig equations. It appears across A-Level and iAL Pure Maths with the major exam boards. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Learn the expansions for sin and cos of a sum and difference, watching the sign — cos of a sum takes a minus. Use them to find exact values by splitting an awkward angle into two familiar ones, and to prove identities.
Before you start
Best tackled after trig identities. You will lean on this again for double angle formulae and R form. This sits in Pure 3.
What you learn
The addition formulae expand sin (A± B), cos (A± B) and tan (A± B). They unlock exact values for angles like 75°, let you prove identities, and turn compound-angle equations into ones you can solve. The formulae are in the exam formula booklet — but the sign flip still catches people out, because they write it from memory under pressure. A standard question gives you one ratio for A and one for B, and asks for sin (A+B), cos (A-B) or tan (A+B). When an equation contains sin (x+30°) or cos (x-45°), you cannot solve it directly. The course works through the addition formulae, finding compound values, proving identities, solving compound-angle equations and problem solving. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Addition Formulae is a Trigonometry topic in the A-level syllabus, covered here at the AS year. You work through 5 concepts and 5 worked examples, testing yourself at 5 points. Students often pair it with Double Angle Formulae, Further Trig Equations and Inverse Trig Functions. Endless extra practice on this strand is available on the Trigonometry revision engine, which generates a fresh question each time.
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