Question

Express sin3theta in terms of sintheta

Answer 1

$\sin3\theta=\sin(\theta+2\theta)=\sin\theta\cos2\theta+\cos\theta\sin2\theta$
$=\sin\theta(1-2\sin^2\theta)+2\cos^2\theta\sin\theta$
$=\sin\theta-2\sin^3\theta+2(1-\sin^2\theta)\sin\theta$
$=3\sin\theta-4\sin^3\theta$