Font (2 3) - + Letter spacing (4 5) - + Word spacing (6 7) - + Line spacing (8 9) - +

Question 5

5. By considering $e^{i\theta}=\cos\theta+i\sin\theta$ or otherwise, show that

\cos^{5}\theta={{1}\over{16}}\cos 5\theta+{{5}\over{16}}\cos 3\theta+{{5}\over% {8}}\cos\theta,

and deduce the indefinite integral

\int\cos^{5}\theta\,d\theta.

[10]