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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.

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

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It is known that a set of turnings of a pane around coordinates origin by various angles has a structure of Abel's group, where composition of consequent counterclockwise turns by angles  and ...

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