It doesn't say "in terms of $\displaystyle \sin^{n-2}(x)$", it says "in terms of $\displaystyle I(n-2)$", and that is what you have done. You're allowed to keep the term $\displaystyle -\frac1n\sin^{n-1}(x)\cos(x)$ in the answer, though perhaps the question could have been worded better, to make that clearer.