We prove the formulae for sin(A+B) and cos(A+B) using Euler's results for sine and cos. The other sum and difference formulae work in a similar way.

Proof of sum and difference formulae for sin and cos using Euler's formulae (MathsCasts)

These MathsCasts were produced by the mathematics support centres at Swinburne University, the University of Limerick and Loughborough University. They were part of a collaborative research project to develop high quality resources and investigate the effectiveness of MathsCasts to support mathematics learning. The full set of resources are available at http://commons.swin.edu.au/s/mathscasts MathsCasts are licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License

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Proof of sum and difference formulae for sin and cos using Euler's formulae (MathsCasts)

Proof of sum and difference formulae for sin and cos using Euler's formulae (MathsCasts)