Question:

<div class='solution'><p><strong>Step 1:</strong> Separate: $\dfrac{dy}{y+1}=-\dfrac{\cos x}{2+\sin x}\,dx$.</p><p><strong>Step 2:</strong> Integrate: $\ln|y+1|=-\ln|2+\sin x|+C$ → $(y+1)(2+\sin x)=K$.</p><p><strong>Step 3:</strong> $y(0)=1$: $2\cdot 2=K=4$. So $y+1=\dfrac{4}{2+\sin x}$. At $x=\pi/2$: $y+1=\dfrac{4}{3}$ → $y=\dfrac{1}{3}$. <strong>Answer: (2)</strong> $1/3$.</p><p class='trap-warning'>⚠️ Trap: Dividing both sides by $2+\sin x$ without recognising $\cos x\,dx = d(\sin x)$ — use substitution $u=\sin x$.</p></div>