A Level Maths: Trigonometry: Compound and Double Angle Formulae Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
- Compound Angle Formulae (Rcos(x) and Rsin(x)) (OCR)
- Compound Angle Formulae (Rcos(x) and Rsin(x)) (Edexcel)
- Compound Angle Formulae (Harder) (OCR)
- Modelling With Trigonometric Functions (Edexcel)
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Trigonometry — foundational trig identities and equations
- Trigonometry — Radians, Circle Sectors and Triangles}}: radian measure is now standard
- Quadratic Equations — needed for the quadratic-in-trig equations that result
A Level Maths trigonometry with compound and double angle formulae is the algebraic powerhouse of Year 2 trigonometry. You learn the formulas for $\sin(A \pm B)$, $\cos(A \pm B)$, and $\tan(A \pm B)$, the double angle formulas, and the harmonic form $R\cos(x \pm \alpha)$. These let you solve a huge range of equations and prove a wide variety of identities.
You apply the compound angle formulas: $\sin(A \pm B) = \sin(A)\cos(B) \pm \cos(A)\sin(B)$ and $\cos(A \pm B) = \cos(A)\cos(B) \mp \sin(A)\sin(B)$. You derive the double angle formulas from these: $\sin(2A) = 2\sin(A)\cos(A)$, $\cos(2A) = \cos^2(A) – \sin^2(A)$ (with two useful alternative forms), and $\tan(2A) = \frac{2\tan(A)}{1 – \tan^2(A)}$. You convert expressions of the form $a\cos(x) + b\sin(x)$ into the harmonic form $R\cos(x – \alpha)$ or $R\sin(x + \alpha)$, where $R = \sqrt{a^2 + b^2}$. This is enormously useful for finding maxima and minima, solving equations of the form $a\cos(x) + b\sin(x) = c$, and modelling oscillating phenomena.
Trigonometry: compound and double angle formulae is part of the Pure Maths strand of A Level Maths for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: $\cos(A – B) = \cos(A)\cos(B) + \sin(A)\sin(B)$ — the sign FLIPS in the cosine formula but not the sine formula; $\cos(2A)$ has three forms — pick the one that matches what is in the equation, especially when integrating; for $R\cos(x – \alpha)$, $R$ is always positive and $\alpha$ is in the first quadrant when both $a$ and $b$ are positive; and double angle does NOT distribute — $\sin(2A)$ is NOT $2\sin(A)$.