CIE A Level Maths: Pure 3

Revision Notes

3.2.1 Compound Angle Formulae

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Compound Angle Formulae

What are the compound angle formulae?

  • There are six compound angle formulae (also known as addition formulae), two each for sin, cos and tan:
  • For sin the +/- sign on the left-hand side matches the one on the right-hand side
sin left parenthesis A plus B right parenthesis identical to sin A cos B plus cos A sin B

sin left parenthesis A minus B right parenthesis identical to sin A cos B minus cos A sin B

  • For cos the +/- sign on the left-hand side is opposite to the one on the right-hand side
cos left parenthesis A plus B right parenthesis identical to cos A cos B minus sin A sin B

cos left parenthesis A minus B right parenthesis identical to cos A cos B plus sin A sin B

  • For tan the +/- sign on the left-hand side matches the one in the numerator on the right-hand side, and is opposite to the one in the denominator
tan left parenthesis A plus B right parenthesis identical to fraction numerator tan A plus tan B over denominator 1 minus tan A tan B end fraction

tan left parenthesis A minus B right parenthesis identical to fraction numerator tan A minus tan B over denominator 1 plus tan A tan B end fraction

  • You can derive the tan identity by:
    • Writing tan left parenthesis A plus B right parenthesis identical to fraction numerator sin left parenthesis A plus B right parenthesis over denominator cos left parenthesis A plus B right parenthesis end fraction
    • Dividing the numerator and denominator by cos A cos B

Exam Tip

  • All these formulae are in the formulae booklet – you don't have to memorise them.

Worked example

Comp Angle Forms Example, A Level & AS Maths: Pure revision notes

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