Help re-writing Trig question

Says to re-write without a fraction.
sin⁡x/(1+cos⁡x )

sinx / (1 + cosx)
Multiply the numerator and denominator by (1 - cosx)
= sinx(1 - cosx) / (1 + cosx)(1 - cosx)
= sinx(1 - cosx) / (1 - cos^2x)
= sinx(1 - cosx) / sin^2x
= (1 - cosx) / sinx
= (1 - cosx)cosecx

i know that sinx=cos(x-90)
this equation might be helpful