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IAL · Pure 3 · Trigonometric Addition Formulae · 4 marks

Prove that sin(A + B) − sin(A − B) = 2 cos A sin B.

Show every step. Do not use a calculator.

👁️ Reveal the mark scheme

M1 — Expand sin(A + B) = sin A cos B + cos A sin B and sin(A − B) = sin A cos B − cos A sin B.

A1 — Subtract: (sin A cos B + cos A sin B) − (sin A cos B − cos A sin B).

M1 — Simplify: the sin A cos B terms cancel.

A1 — Leaves 2 cos A sin B ✓. QED.

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