- Prove DeMoivre’s theorem,
for all
and all
.
- Prove the triple angle formulas for sine and cosine,
by letting
in part (a).
- Proof. Since
we have
- Letting
, we first apply DeMoivre’s theorem to get
On the other hand, we can expand the product,
Equating real and imaginary parts from the two expressions we obtain the requested identities: