sin2X = sin2X
What is it about ' equation ' you do you not understand. Of course they are equal!
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1 - sin2x(1+ cos2x)/2
(1 - tan2x)/(1 + tan2x) = (1 - sin2x/cos2x)/(1 + sin2x/cos2x) = (cos2x - sin2x)/(cos2x + sin2x) = (cos2x - sin2x)/1 = (cos2x - sin2x) = cos(2x)
sin2x because sin2x + cos2x = 1
Use this identity sin2x+cos2x=1 sin2x=1-cos2x so sin2x/(1-cosx) =(1-cos2x)/(1-cosx) =(1-cosx)(1+cosx)/(1-cosx) =1+cosx
sin2x is the conventional way of writing (sinx)2; it does not denote the sine of sinx as one might expect. So the square root is just sinx.