Posted by noel on Friday, June 22, 2012 at 5:06pm.
1. The way you typed it, the identity is false, but I am sure you meant
tanx = (sinx + sin^2x)/(cosx(1 + sinx))
RS = sinx(1 + sinx) / (cosx(1+sinx))
= sinx/cosx
= tanx
= LS
2. LS = cosx(cos^2x + sin^2x)
= (cosx)(1)
= cosx
RS = 1/secx
= cosx
= LS