Prove:

(tanx)(sinx) / (tanx) + (sinx) = (tanx) - (sinx) / (tanx)(sinx)

What I have so far:

L.S.

= (sinx / cosx) sinx / (sinx / cosx) + sinx

= (sin^2x / cosx) / (sinx + (sinx) (cosx) / cosx)

= (sin^2x / cosx) / (cosx / sinx + sinxcosx)

What do I do now and if I did something wrong, where did I go wrong and how should I go about to fix it?