sin2x = sinxcosx+sinxcosx=2sinxcosx=(2sinxcosx)/1 = 2sinxcosx/(cos^2x+sin^2x) Devide both numerator and denominator by cos^2x we have sin2x = 2sinxcosx/cos^2x)/[(cos^2x+sin^2x)/cos^2x] = (2sinx/cosx)/[(cos^2x/cos^2x)+(sin^2x/cos^2x)] = 2tanx/(1+tan^2x)