Question

Use De Moivre's Theorem to express cos 6∅ in terms of sums and differences of powers of sin∅ and cos∅

Answer 1

\[\Large
[r(\cos \theta+i\sin\theta)]^n = r^n(\cos n\theta+i\sin n\theta)
\]

Answer 2

follow @wio 's idea.

set \(\large r=1\)

\[\large (\cos \theta + i\sin \theta)^n=\cos(n\theta)+i\sin(n\theta)\]
expand the left hand side, then compare (and equate) real parts of the complex numbers

Answer 3

ok will do thanks guys.