1-cos (2A)/2sin A+ SIN (2A)= tan (A/2)

I need to verify the identity I have no idea how to do that and I have a test please explain!!!

you need to review your double and half angle formulas:

tan(A/2) = (1-cosA)/sinA = sinA/(1+cosA)

cos(2A) = 2cos^2A-1 = 1-2sin^2A = cos^2A-sin^2A

sin2A = 2sinAcosA

A little playing around with those should help.

Also, you need some parentheses to make it clear just what the fractions are...