I realize that some of you consider this very basic but I'm wondering if $\displaystyle \csc\theta=\frac{1}{\sin\theta}$

would it follow that $\displaystyle \csc^2\theta=\frac{1}{\sin^2\theta}$?

I guess the real question I'm wondering is whether or not I can use trig identities, regardless of the power of the identities being used, as long as all the identities are raised to the same power?