Question
Prove that the function $f(x)=\log (\sin x)$ is increasing in the interval $\left(0, \frac{\pi}{2}\right)$.
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| $X:$ | $0.5$ | $1$ | $1.5$ | $2$ |
| $P(X):$ | $k$ | $k^2$ | $2k^2$ | $k$ |