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Trigonometry: Addition Theorems

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Deduce the addition theorems for trigonometric functions:

cos (x ± y) = cosx cosy sinx siny;

sin (x ± y) = sinx cosy ± cosx siny

as the simplest consequence of the representation of a complex plane's rotational group.


Solution Summary

Addition theorems for trigonometric functions are deduced.
The solution is detailed and well presented.