Posted by tatiana on Monday, October 3, 2011 at 8:26pm.
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