Problem

(a) Use the definition of $\sinh x$ in terms of exponentials to show that

$$\sinh 3x \equiv 4\sinh^3 x + 3\sinh x.$$

(b) Hence determine the exact coordinates of the points of intersection of the curve with equation $y = \sinh 3x$ and the curve with equation $y = 19\sinh x$, giving your answers as simplified logarithms where necessary.