>>221
t = tan(x/2)
dt/dx = (1+t^2)/2
(1+t^2)dx = 2 dt
sin(x) = 2sin(x/2)cos(x/2) = 2t {cos(x/2)^2} = 2t/(1+t^2)
1+sin(x) = {(1+t)^2}/(1+t^2)
dx/{1+sin(x)} = (1+t^2)dx/{(1+t)^2} = 2dt/{(1+t)^2}