Use the following Properties:
1. Quotient Property:
#tan x = sinx /cos x#
2. Pythagorean Property:
#cos^2x + sin^2 x =1#
3. Double Argument Property
#cos 2x = cos^2x-sin^2 x#
LEFT HAND SIDE:
#(1-tan^2(x/2))/(1+tan^2(x/2)) = (1-sin^2(x/2)/cos^2(x/2))/(1+sin^2(x/2)/cos^2(x/2))#
#=((cos^2(x/2)-sin^2(x/2))/cos^2(x/2))/((cos^2(x/2)+sin^2(x/2))/cos^2(x/2))#
#=(cos^2 (x/2)-sin^2(x/2))/(cos^2(x/2))*(cos^2(x/2))/(cos^2(x/2)+sin^2(x/2)#
#=(cos^2 (x/2)-sin^2(x/2))/cancel(cos^2(x/2))*cancel(cos^2(x/2))/(cos^2(x/2)+sin^2(x/2)#
#=(cos^2 (x/2)-sin^2(x/2))/(cos^2(x/2)+sin^2(x/2)#
#=(cos2(x/2))/1#
#=(coscancel2(x/cancel2))/1#
#= cos x#
#:.=# RIGHT HAND SIDE
