Factor First

When every term shares a trig factor, take it out: the bracket left behind is often an identity. Prove ${\sin\left(x\right)}^{3}+\sin\left(x\right){\cos\left(x\right)}^{2} = \sin\left(x\right)$. Both terms hold a sin x, so Take out the common trig factor: $\sin\left(x\right)\left({\sin\left(x\right)}^{2}+{\cos\left(x\right)}^{2}\right)$. The bracket is 1, and sin x times 1 is sin x.

Factoring keeps the value; dividing does not. Dividing the expression by sin x would change what it equals, and lose the angles where sin x is 0. Take the factor out and keep it on the line.