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 | - |