How do I prove that sinx/sinx+cosx=tanx/1+tanx

Answer 1

I am sure you meant to say
sinx/(sinx+cosx) = tanx/(1+tanx)

RS = (sinx/cosx)/[1 + sinx/cosx]
= (sinx/cosx)/[(cosx+sinx)/cosx]
= (sinx/cosx) ( cosx/(cosx + sinx))
= sinx/(cosx + sinx)
= LS