7.2PureStretch

Using the Addition Formulae

The addition formulae are used to prove identities, simplify expressions and solve equations. This lesson focuses on applying them confidently in both directions.

26 min Trigonometry and Modelling

Edexcel A level Maths: 7.2 Using the Addition FormulaeCurated by Kepler, not produced by us. Watch it before the notes below.

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What you'll be able to do

Apply the formulae to prove identities
Simplify combined expressions
Recognise an expansion in reverse
Solve equations using compound angles

Reading the formulae in reverse

A combination like $sin A cos B + cos A sin B$ collapses to $sin (A + B)$ . Spotting these reversed forms is half the skill.

sin A cos B + cos A sin B = sin (A + B)

Recognise the pattern backwards.

1Matches

cos (A + B)

with

A = 50°, B = 10°

= cos 60° = \frac{1}{2}

Answer

\frac{1}{2}

Proving identities

Expand both compound angles, then simplify using $sin^{2} + cos^{2} = 1$ and other known identities.

Tip — When an expression has products of sin and cos of two angles, suspect an addition formula in reverse.

Formula recap

cos A cos B - sin A sin B = cos (A + B)

Reverse cosine.

sin A cos B + cos A sin B = sin (A + B)

Reverse sine.

Common mistakes to avoid

Not recognising a reversed expansion.

Products like cosAcosB − sinAsinB collapse to cos(A+B).

Mismatching the sign when collapsing.

A minus between the products means cosine of a sum.

Key takeaways

Use the formulae forwards and backwards.
cosAcosB − sinAsinB = cos(A+B); sinAcosB + cosAsinB = sin(A+B).
Collapse products to a single compound angle to simplify.

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Real past-paper questions on Using the Addition Formulae, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.

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Using the Addition Formulae

Reading the formulae in reverse

Proving identities

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Using the Addition Formulae

Reading the formulae in reverse

Proving identities

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