From the fundamental identities, we know that
[tex]csc\varphi=\frac{1}{sin\varphi}[/tex]
By substituting this result into the given expression, we have
[tex]9sin\varphi(\frac{1}{sin\varphi}-sin\varphi)[/tex]
Now, by distributing sine of phi into the parentheses, we have
[tex]9(\frac{sin\varphi}{sin\varphi}-sin^2\varphi)[/tex]
or equivalently,
[tex]9(1-sin^2\varphi)[/tex]
Now, from the Pythagorean identity:
[tex]cos^2\varphi+sin^2\varphi=1[/tex]
we can note that
[tex]cos^2\varphi=1-sin^2\varphi[/tex]
Then, by substituting this result into our last result from above, we obtain
[tex]9(1-sin^2\varphi)=9cos^2\varphi[/tex]
Therefore, the answer is:
[tex]9cos^2\varphi[/tex]
