Addition Formulae

This lesson covers the addition (compound angle) formulae for sin, cos, and tan. These formulae allow you to expand expressions like sin(A + B) and cos(A − B), and they are fundamental to much of the trigonometry at A-Level — including double angle formulae, the R cos(θ + α) form, and proving identities.

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The Formulae

Sine Addition Formulae

sin(A + B) ≡ sin A cos B + cos A sin B
sin(A − B) ≡ sin A cos B − cos A sin B

Cosine Addition Formulae

cos(A + B) ≡ cos A cos B − sin A sin B
cos(A − B) ≡ cos A cos B + sin A sin B

Note the sign pattern: in the cos formulae, the sign in the expansion is opposite to the sign in the argument.

Tangent Addition Formulae

tan(A + B) ≡ (tan A + tan B) / (1 − tan A tan B)
tan(A − B) ≡ (tan A − tan B) / (1 + tan A tan B)

These formulae are in the AQA formula booklet, but you must be able to use them fluently.