Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2015 / Paper 1 / 15 / c / i / Solution

Use the Maclaurin series $\sin x=x-x^3/6+O(x^5)$ and $(1+x{)}^{-2}=1-2x+3x^2+O(x^3)$. Multiplying through the cubic order givesThese are the first three nonzero terms; the constant term vanishes.