sin2x/2cosx(1+tanxtanx/2) =2sinxcosx/2cosx(1+tanxtanx/2) =sinx/(1+tanxtanx/2) =sinx/(1+2tanx/2^2/(1-tanx/2^2)] =sinx/[(1+tanx/2^2)/(1-tanx/2^2)] =sinx*(1-tanx/2^2)/(1+tanx/2^2) =sinx*cosx=1/2sin2x