These formulae are often refered to as the addition formulae:
\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B
\cos(A \pm B) = \cos A \cos B \mp \sin A \sin B
\tan(A \pm B) = \displaystyle \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}
\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B
\cos(A \pm B) = \cos A \cos B \mp \sin A \sin B
\tan(A \pm B) = \displaystyle \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}
Software/Applets used on this page
Glossary
addition formulae
the trigonometrical formulae:
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-cosAsinB
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-cosAsinB
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
union
The union of two sets A and B is the set containing all the elements of A and B.
This question appears in the following syllabi:
| Syllabus | Module | Section | Topic | Exam Year |
|---|---|---|---|---|
| AP Calculus AB (USA) | 1 | Trigonometry | Addition formulae | - |
| AP Calculus BC (USA) | 1 | Trigonometry | Addition formulae | - |
| AQA A-Level (UK - Pre-2017) | C4 | Trigonometry | Addition formulae | - |
| AQA A2 Maths 2017 | Pure Maths | Further Trigonometry | Addition Formulae | - |
| AQA AS/A2 Maths 2017 | Pure Maths | Further Trigonometry | Addition Formulae | - |
| CBSE XI (India) | Sets and Functions | Trigonometric Functions | Addition identities e.g. sinx +siny sin(x+y) etc. | - |
| CCEA A-Level (NI) | C4 | Trigonometry | Addition formulae | - |
| CIE A-Level (UK) | P2 | Trigonometry | Addition formulae | - |
| Edexcel A-Level (UK - Pre-2017) | C3 | Trigonometry | Addition formulae | - |
| Edexcel A2 Maths 2017 | Pure Maths | Trigonometric Problem Solving | Addition Formulae | - |
| Edexcel AS/A2 Maths 2017 | Pure Maths | Trigonometric Problem Solving | Addition Formulae | - |
| I.B. Higher Level | 3 | Trigonometry | Addition formulae | - |
| Methods (UK) | M2 | Trigonometry | Addition formulae | - |
| OCR A-Level (UK - Pre-2017) | C3 | Trigonometry | Addition formulae | - |
| OCR A2 Maths 2017 | Pure Maths | Further Trig Identities and Equations | Addition Formulae | - |
| OCR MEI A2 Maths 2017 | Pure Maths | Further Trig Identities and Equations | Addition Formulae | - |
| OCR-MEI A-Level (UK - Pre-2017) | C4 | Trigonometry | Addition formulae | - |
| Pre-Calculus (US) | C4 | Trigonometry | Addition formulae | - |
| Pre-U A-Level (UK) | 2 | Trigonometry | Addition formulae | - |
| Scottish (Highers + Advanced) | HM2 | Trigonometry | Addition formulae | - |
| Scottish Highers | M2 | Trigonometry | Addition formulae | - |
| Universal (all site questions) | T | Trigonometry | Addition formulae | - |
| WJEC A-Level (Wales) | C4 | Trigonometry | Addition formulae | - |