We multiply numerator (top) and denominator (bottom) of the right hand side of our first result by `1+cos alpha`, and obtain:

`(1-cos alpha)/(sin alpha) xx (1+cos alpha)/(1+cos alpha)`

Next, we use the difference of 2 squares.

`=(1-cos^2alpha)/(sin alpha(1+cos alpha))`

We recall `sin^2θ + cos^2θ = 1`, and use it to obtain:

`=(sin^2alpha)/(sin alpha(1+cos alpha))`

Finally, we cancel out the sin α.

`=(sin alpha)/(1+cos alpha`