Prove that: `int_(0)^(pi//2) log (sin x) dx =int_(0)^(pi//2) log (cos x) dx =(-pi)/(2) log 2`

Explanation

To prove that

\[ \int_{0}^{\frac{\pi}{2}} \log(\sin x) \, dx = \int_{0}^{\frac{\pi}{2}} \log(\cos x) \, dx = -\frac{\pi}{2} \log 2, \]

we will follow these steps:

...