By using the properties of definite integrals, evaluate the integrals`int_0^(pi/2) (sinx-cosx)/(1+sinxcosx)dx`

Explanation

To evaluate the integral \( I = \int_0^{\frac{\pi}{2}} \frac{\sin x - \cos x}{1 + \sin x \cos x} \, dx \) using the properties of definite integrals, we can follow these steps:

### Step 1: Set up the integral
We start with the integral:
\[ I = \int_0^{\frac{\pi}{2}} \frac{\sin x - \cos x}{1 + \sin x \cos x} \, dx \]

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