Combine $\sin\left(x\right)+\frac{\cos\left(x\right)^2}{\sin\left(x\right)}$ in a single fraction

When multiplying two powers that have the same base ($\sin\left(x\right)$), you can add the exponents

Applying the pythagorean identity: $\sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1$

Divide fractions $\frac{1}{\frac{1}{\sin\left(x\right)}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$