sin 化成 tan

sina=2sin(a/2)cos(a/2)
=2sin(a/2)cos(a/2)/[sin^2(a/2)+cos^2(a.2)]
=2tan(a/2)/[1+tan^2(a/2)]

tanx=sinx/cosx=sinx/(根号下1-cosx平方）

sin(x) = 2sin(x/2)cos(x/2)

= 2[sin(x/2)/cos(x/2)]/[cos(x/2)]^(-2)

= 2tan(x/2)/[sec(x/2)]^2

= 2tan(x/2)/{1 + [tan(x/2)]^2}

sin2x=2sinx*cosx
sinx=1-tanx/1+tanx