2024 SJI P2 Q3

Show that \(\dfrac{\mathrm d}{\mathrm dx}\left(\dfrac{\cos x}{1+\sin x}\right)=\dfrac{-1}{1+\sin x}\).[2]

Using l’Hôpital’s rule, find \(\displaystyle\lim_{x\to0}\dfrac{\ln(1+\sin x)-x}{x^2}\).[4]