Prove the identity sinx + tanx = tanx(cosx + 1)

I tried to prove each identity but I'm not sure if there right

1) sinx + tanx = tanx(cosx + 1)
LS = sinx + tanx tanx(cosx + 1)
= sinx + (sinx/cosx)
= sinx/1 + cosx
Not sure what to do next?

2) tanθ - 1 = sin^2θ - cos^2θ/sinθcosθ + cos^2θ
what i ended up with:
LS = sinθ/cosθ - 1 RS = sin^2θ - cos^2θ/sinθcosθ + cos^2θ
what next?

Thanks for trying:)

LHS
-------
sin x + sin x / cos x

sin x cos x + sin x
-----------------------
cos x

sin x ( cos x + 1 )
----------------------
cos x

tan x ( cos x + 1 )

1)sinx = tanx(cosx+1-1){take tanx to the other side}
sin x = tanx cosx = sinx
so LHS =RHS
2)not clear