@logx

cos x = 1 t 2 1 + t 2
cos x = cos 2 x 2 sin 2 x 2
       = cos 2 x 2 ( 1 sin 2 x 2 cos 2 x 2 )
1+ tan 2 x 2 = 1 cos 2 x 2
       = 1 tan 2 x 2 1 + tan 2 x 2