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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}
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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

union

The union of two sets A and B is the set containing all the elements of A and B.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopic
AP Calculus AB (USA)1TrigonometryAddition formulae
AP Calculus BC (USA)1TrigonometryAddition formulae
AQA A-Level (UK - Pre-2017)C4TrigonometryAddition formulae
AQA A2 Maths 2017Pure MathsFurther TrigonometryAddition Formulae
AQA AS/A2 Maths 2017Pure MathsFurther TrigonometryAddition Formulae
CBSE XI (India)Sets and FunctionsTrigonometric FunctionsAddition identities e.g. sinx +siny sin(x+y) etc.
CCEA A-Level (NI)C4TrigonometryAddition formulae
CIE A-Level (UK)P2TrigonometryAddition formulae
E TrigonometryE6 Compound Angle FormulaeAddition Formulae
Edexcel A-Level (UK - Pre-2017)C3TrigonometryAddition formulae
Edexcel A2 Maths 2017Pure MathsTrigonometric Problem SolvingAddition Formulae
Edexcel AS/A2 Maths 2017Pure MathsTrigonometric Problem SolvingAddition Formulae
I.B. Higher Level3TrigonometryAddition formulae
Methods (UK)M2TrigonometryAddition formulae
OCR A-Level (UK - Pre-2017)C3TrigonometryAddition formulae
OCR A2 Maths 2017Pure MathsFurther Trig Identities and EquationsAddition Formulae
OCR MEI A2 Maths 2017Pure MathsFurther Trig Identities and EquationsAddition Formulae
OCR-MEI A-Level (UK - Pre-2017)C4TrigonometryAddition formulae
Pre-Calculus (US)C4TrigonometryAddition formulae
Pre-U A-Level (UK)2TrigonometryAddition formulae
Scottish (Highers + Advanced)HM2TrigonometryAddition formulae
Scottish HighersM2TrigonometryAddition formulae
Universal (all site questions)TTrigonometryAddition formulae
WJEC A-Level (Wales)C4TrigonometryAddition formulae