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The double angle formulae express sin 2x, cos 2x and tan 2x in terms of a single angle x, and follow directly from the addition formulae. They are used to simplify trigonometric expressions, prove identities, integrate trig functions and solve equations mixing single and double angles. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
These come from the addition formulae with both angles equal. Cos of a double angle has three forms; choose the one that leaves you with the function you want. They are also what let you integrate even powers of sine and cosine.
Before you start
This builds directly on the addition formulae. It is Pure 3 content. It reappears throughout solving equations and integration. Filed under Trigonometry.
What you learn
The double angle formulae come straight from the addition formulae by setting B=A. Cosine has three forms, and knowing which to pick is the whole skill. The course works through where the formulae come from, the three forms of cos 2A, rearranging: the power-reduction forms, solving: factorise, never divide and proof and synthesis. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Double Angle Formulae is a Trigonometry topic in the A-level syllabus, covered here at the AS year. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. Students often pair it with Further Trig Equations, Inverse Trig Functions and R sin(θ + α) Form. For unlimited practice, the Trigonometry revision engine builds new questions on demand and records your accuracy.
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