Hello, Tutu!

2) How do I, using complex number methods, deduce that:

You should be familiar with this identity: .

For , we have: . .[1]

Expand the left side:

. .

n . . . . . . . . . . . .

Then [1] becomes: .

Equate real and imaginary components:

. . Hence: .

. . Hence: .

And we have the Triple-angle Identities for both sine and cosine.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Divide top and bottom by

Therefore: .