Fundamentals and Basic Identities

To reduce ${\displaystyle \frac{{\sin }^2<!--\; \; -->x-<!--\; -\; -->9}{\sin <!--\; \; -->x-<!--\; -\; -->3}}$, factor the numerator: ${\displaystyle \frac{(\sin <!--\; \; -->x-<!--\; -\; -->3)(\sin <!--\; \; -->x+3)}{\sin <!--\; \; -->x-<!--\; -\; -->3}}$

Notice that we can cancel out a sinx−3.

This leaves us with sinx+3.