(a)[3]
Using the expansions of $\sin(3x + 2x)$ and $\sin(3x - 2x)$, show that the identity $\tfrac{1}{2}(\sin 5x + \sin x) = \sin 3x \cos 2x$ holds.
(b)[3]
Hence show that the value of $\int_{0}^{\tfrac{1}{4}\pi} \sin 3x \cos 2x\, dx$ is $\tfrac{1}{5}(3 - \sqrt{2})$.