Proving identity

(sinx+tanx)/(cosx+1)=tanx
RS: (sinx+(sinx/cosx))/(cosx+1)
((sinxcosx/cosx)+(sinx/cosx))x 1/(cosx+1)
sinx(cosx+1)/cosx x 1/(cosx+1)
sinx/cosx = tanx
RS = LS

How did sinxcosx/cosx turn to sinx(cosx+1)?

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