A Difference of Squares

In algebra, $\left(a-b\right)\left(a+b\right) = {a}^{2}-{b}^{2}$. This is called a difference of squares. It works the same with a trig function in place of b: $\left(1-\sin\left(x\right)\right)\left(1+\sin\left(x\right)\right) = 1-{\sin\left(x\right)}^{2}$. Then the identity turns this into ${\cos\left(x\right)}^{2}$.

Look for a square minus 1, or 1 minus a square. For example, $\left(\csc\left(x\right)-1\right)\left(\csc\left(x\right)+1\right) = {\csc\left(x\right)}^{2}-1$, which is ${\cot\left(x\right)}^{2}$.