Double Angle Formulae (Cambridge International A-Level Mathematics)

Double angle formulae

What are the double angle formulae?

• The double angle formulae are derived from the 'A+B' versions of the compound angle formulae:

  • sin (2 A) ≡ 2 sin A cos A

  • $\mathrm{cos}(2A)\equiv\mathrm{cos}^{2}A-\mathrm{sin}^{2}A$

    • $\mathrm{cos}(2A)\equiv2\mathrm{cos}^{2}A-1$
    • $\mathrm{cos}(2A)\equiv1-2\mathrm{sin}^{2}A$

  • $\mathrm{tan}(2A)\equiv\frac{2\mathrm{tan}A}{1-\mathrm{tan}^{2}A}$

Exam Hint

• The double angle formulae can be found in the formulae booklet – make sure you know where to find them.
• Look out for problems containing sinAcosA or an equation that contains both a double angle and a single angle.

Worked Example