Hi

I have the answer in the textbook for this one but I am hoping someone can explain it to me.

integral sign (sin x/ (1+ cos^2 x) dx =

integral sign ((sin x cos x)/(1+cos^2 x)dx

why was cos x "added" to the numerator - it wasn't "added" to the denominator - it just seems to come out of no where.

Any enlightenment would be appreciated.