Exercise 2.10

Derive the formulae for sin x and cos x in terms of exp ix and exp(-ix), that follows from equation (A) above.


Equation (A) reads

exp ix  =  cos x + i sin x

and it holds for all x positive or negative, so that we also have

exp(-ix) =  cos x - i sin x

where we have used the fact that cosine is an even function and sine an odd one.

We can solve these two equations for cos x and sin x