$\displaystyle\int_0^{\pi/2}\dfrac{\sin x-\cos x}{1+\sin x\cos x}dx=$
Step-by-Step Solution
Key Concept: Use $I=\int_0^{\pi/2}f(x)dx$ and replace $x\to\pi/2-x$: integrand becomes negative; $2I=0$
$f(\pi/2-x)=\frac{\cos x-\sin x}{1+\sin x\cos x}=-f(x)$. So $2I=0\Rightarrow I=0$.
Correct Answer: 3