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:)
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 )

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+11){take tanx to the other side}
sin x = tanx cosx = sinx
so LHS =RHS
2)not clear
sin x = tanx cosx = sinx
so LHS =RHS
2)not clear