What mistakes do students make with Trigonometry?

Writing cos(A + B) = cos A cos B + sin A sin B instead of the correct cos A cos B − sin A sin B. The cosine addition formula has a minus sign. Forgetting the factor 2 in sin 2A = 2 sin A cos A, or writing sin 2A = sin A cos A; the double angle formula includes the factor 2. When converting a cos θ + b sin θ to R sin(θ + α), using tan α = b/a instead of tan α = a/b. Check by expanding R sin(θ + α) and comparing coefficients.

What are the exam tips for Trigonometry in Mathematics Pearson Edexcel A-Level?

The addition formulae are given in the formula booklet, but you must know how to derive the double angle formulae from them. When using harmonic form, clearly show the expansion of R cos(θ ± α) or R sin(θ ± α) and equate coefficients to find R and α.

Pearson Edexcel · A-Level · Mathematics

Course version: 9MA0 · Version from Mar 2026

Understand and use double angle formulae; use of formulae for sin(A ± B),…

Full specification wording

Trigonometry: 5.6 Understand and use double angle formulae; use of formulae for sin(A ± B), cos(A ± B), and tan(A ± B); understand geometrical proofs of these formulae. Understand and use expressions for a cos θ + b sin θ in the equivalent forms of R cos(θ ± α) or R sin(θ ± α).

Addition formulae are sin(A ± B) = sin A cos B ± cos A sin B, cos(A ± B) = cos A cos B ∓ sin A sin B, and tan(A ± B) = (tan A ± tan B)/(1 ∓ tan A tan B).

Checked against the Pearson Edexcel 9MA0 specification (opens in a new tab) on 25 September 2026.

Point 6 of 9
2 key terms

Study notes

From the checked teaching notes for this specification point.

The idea

What earns the marks

Correctly state and apply the addition formulae for sin(A ± B), cos(A ± B) and tan(A ± B), including the sign changes in the cosine and tangent formulae.
Derive the double angle formulae by substituting B = A into the addition formulae, and select the appropriate form of cos 2A for a given problem.
Construct geometrical proofs of the addition formulae by drawing stacked right-angled triangles and resolving lengths to find sin(A + B) and cos(A + B).
Convert a cos θ + b sin θ into R cos(θ ± α) or R sin(θ ± α) by equating coefficients, calculating R = √(a² + b²) and determining α using the correct ratio.
Solve equations or find maxima/minima of expressions like a cos θ + b sin θ using the harmonic form.

Common mistakes and how to put them right

Writing cos(A + B) = cos A cos B + sin A sin B instead of the correct cos A cos B − sin A sin B.
Put it right: The cosine addition formula has a minus sign.
Forgetting the factor 2 in sin 2A = 2 sin A cos A, or writing sin 2A = sin A cos A; the double angle formula includes the factor 2.
When converting a cos θ + b sin θ to R sin(θ + α), using tan α = b/a instead of tan α = a/b.
Put it right: Check by expanding R sin(θ + α) and comparing coefficients.

Exam tips

The addition formulae are given in the formula booklet, but you must know how to derive the double angle formulae from them.
When using harmonic form, clearly show the expansion of R cos(θ ± α) or R sin(θ ± α) and equate coefficients to find R and α.

Try the lesson

The start of the Trigonometry: 5.6 Understand and use double angle formulae; use of formulae for sin(A ± B), cos(A ± B), and tan(A ± B); understand geometrical proofs of these formulae. Understand and use expressions for a cos θ + b sin θ in the equivalent forms of R cos(θ ± α) or R sin(θ ± α). lesson, made from checked teaching notes for this specification point.

Have a go first

Given that sin θ = 3/5 and θ is acute, use a double angle formula to find the exact value of sin 2θ.

Tip: press 1 to 4 to choose

Listen

Addition formulae are sin(A ± B) = sin A cos B ± cos A sin B, cos(A ± B) = cos A cos B ∓ sin A sin B, and tan(A ± B) = (tan A ± tan B)/(1 ∓ tan A tan B). Setting B = A gives double angle results like sin 2A = 2 sin A cos A. Geometrical proofs of addition formulae use stacked right-angled triangles: a triangle with angle B sits on the hypotenuse of one with angle A. Resolving sides derives sin(A + B) and cos(A + B). The harmonic form a cos θ + b sin θ (for a, b > 0) can be expressed as R cos(θ − α) where R = √(a² + b²) and tan α = b/a, or R sin(θ + α) where tan α = a/b. For example, 3 cos θ + 4 sin θ = 5 cos(θ − 53.1°) since R = √(3²+4²) = 5 and tan α = 4/3. Other sign combinations map to R cos(θ + α) or R sin(θ − α). A strong answer earns marks for these points. Correctly state and apply the addition formulae for sin(A ± B), cos(A ± B) and tan(A ± B), including the sign changes in the cosine and tangent formulae. Derive the double angle formulae by substituting B = A into the addition formulae, and select the appropriate form of cos 2A for a given problem. Construct geometrical proofs of the addition formulae by drawing stacked right-angled triangles and resolving lengths to find sin(A + B) and cos(A + B). Convert a cos θ + b sin θ into R cos(θ ± α) or R sin(θ ± α) by equating coefficients, calculating R = √(a² + b²) and determining α using the correct ratio. Exam tip: The addition formulae are given in the formula booklet, but you must know how to derive the double angle formulae from them.

See it

A top-down flowchart. The top node reads 'Addition formulae for sin(A ± B), cos(A ± B), tan(A ± B)'. Two arrows lead from it. The first goes to 'Set B = A', which leads to 'Double angle formulae, e.g. sin 2A = 2 sin A cos A'. The second goes to 'Geometrical proof: stacked right-angled triangles', which leads to 'Resolve sides to derive sin(A + B) and cos(A + B)'. Separately, a node 'a cos θ + b sin θ' has two arrows: one to 'R cos(θ − α): R = √(a² + b²), tan α = b/a' and one to 'R sin(θ + α): tan α = a/b'. — It shows how the addition formulae lead to the double angle formulae and geometrical proofs, and how a cos θ + b sin θ converts into harmonic form.

Key words

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Double angle formulae

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Geometrical proofs

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See every definition

Double angle formulae: Results such as sin 2A = 2 sin A cos A, obtained by setting B = A in the addition formulae.
Geometrical proofs: Proofs of the addition formulae using stacked right-angled triangles, where a triangle with angle B sits on the hypotenuse of one with angle A, and resolving sides derives sin(A + B) and cos(A + B).

Label the diagram

Some boxes have lost their names. Pick the right name for each number.

The diagram again, with 3 boxes numbered instead of named. A top-down flowchart. The top node reads 'Addition formulae for sin(A ± B), cos(A ± B), tan(A ± B)'. Two arrows lead from it. The first goes to 'Set B = A', which leads to 'Double angle formulae, e.g. sin 2A = 2 sin A cos A'. The second goes to 'Geometrical proof: stacked right-angled triangles', which leads to 'Resolve sides to derive sin(A + B) and cos(A + B)'. Separately, a node 'a cos θ + b sin θ' has two arrows: one to 'R cos(θ − α): R = √(a² + b²), tan α = b/a' and one to 'R sin(θ + α): tan α = a/b'.

1Box 1
2Box 2
3Box 3

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Test your understanding of Trigonometry: 5.6 Understand and use double angle formulae; use of formulae for sin(A ± B), cos(A ± B), and tan(A ± B); understand geometrical proofs of these formulae. Understand and use expressions for a cos θ + b sin θ in the equivalent forms of R cos(θ ± α) or R sin(θ ± α).

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