Prove the following trigonometric identities

Question

1. tanx = sinx + sin^2x/cosx(1+sinx)

2. cos^3+(cosx)(sin^2x) = 1/secx

Answer 1

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