eagle SG 1 - cos x = 2 ( sin (x/2) )^2 ----- (1) sinx = 2 sin (x/2) cos (x/2) ------ (2) dividing (1) / (2) gives you tan (x/2)
eagle SG tan A sin A + cos A -1 = (sin A )^2 / cos A + cos A -1 = { (sin A )^2 + (cos A )^2 } / cos A - 1 = 1 / cos A - 1 = sec A - 1