[not sure if this would come under trig identities, (part B of this question is differentiation, but i'm not needing help with that)]
you have the identity that:
$\displaystyle \sin^2(x)+\cos^2(x)=1$
so then $\displaystyle \cos^2(x)=1-\sin^2(x)$
so we then have:
$\displaystyle
\frac{\sin^3(x)}{\sin^2(x)}+\frac{1}{\sin^2(x)}{\c olor{blue} -\frac{\sin^2(x)}{\sin^2(x)}}$
so:
$\displaystyle {\color{blue} - \frac{\sin^2(x)}{\sin^2(x)}=-1}$