From the Pythagorean identity,
[tex]\sin ^2\beta+\cos ^2\beta=1[/tex]
we have
[tex]\sin ^2\beta=1-\cos ^2\beta[/tex]
Then, the given expression can be rewritten as
[tex]\cot ^2\beta\sin ^2\beta\ldots(a)[/tex]
On the other hand, we know that
[tex]\begin{gathered} \cot \beta=\frac{\cos\beta}{\sin\beta} \\ \text{then} \\ \cot ^2\beta=\frac{\cos^2\beta}{\sin^2\beta} \end{gathered}[/tex]
Then, by substituting this result into equation (a), we get
[tex]\begin{gathered} \frac{\cos^2\beta}{\sin^2\beta}\sin ^2\beta \\ \frac{\cos ^2\beta\times\sin ^2\beta}{\sin ^2\beta} \end{gathered}[/tex]
so by canceling out the squared sine, we get
[tex]\cos ^2\beta[/tex]
Therefore, the answer is the last option
