Which double-angle or half-angle identity would you use to verify that

RTP: 1 + cos2x = 2/1+tan^2x

LHS  =  1 + cos2x
         =  1 + 2cos^2x - 1
         =  2cos^2x

RHS = 2/1+tan^2x
         = 2/sec^2x
         = 2 x cos^2x
         = 2cos^2x

2cos^2x=2cos^2x
LHS = RHS