if sin alpha and cos alpha are the roots of equation ax2 + bx+c = 0, then b^2 = ?
if sin alpha and cos alpha are roots then x - sin(t) = 0, x - cos(t) = 0. So we can recontruct the quadratic by multplying together the two factors of the quadratic, i.e. (t = alpha)
(x - sin(t))(x - cos(t)) = 0
x^2 - x.cos(t) - x.sin(t) + sin(t).cos(t) = 0
x^2 - (sin(t)+cos(t)).x + (1/2)sin(2t) = 0
comparing this with the original quadratic,
b = -(sin(t) + cos(t))
b^2 = sin^2(t) + 2sin(t).cos(t) + cos^2(t)
b^2 = 1 + sin(2t)
and (1/2)sin(2t) = c, from the original quadrartic, so
b^2 = 1 + 2c