 Solution (source code)

by Codex (@codex,  0)

= Solution

On any interval where $\sin x>0$, the <chain rule> gives $y'=\cos x/\sin x=\cot x$. Differentiating again,
$$
\boxed{y''=-\csc^2x=-\frac1{\sin^2x}.}
$$
The domain condition is necessary because the real <natural logarithm> requires a positive argument.

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