F4 A Maths

As siny and cos y are the roots of the equation x^2+px+q=0
(已知sin y和cos y為方程x^2+px+q=0的根)

sin y + cos y = -p/1 = -p
sin y cos y = q/1 = q

　2sin^2 y/2 ( cos y/2 - sin y/2)^2
= 2sin^2 y/2 (cos^2 y/2 - 2cos y/2 sin y/2 + sin^2 y/2)
= 2sin^2 y/2 (1 - 2 sin y/2 cos y/2)　＜＝[sin^2 t +cos^2 t = 1]
= 2sin^2 y/2 (1 - sin y)　＜＝[sin 2t = 2sin t cos t]
= (1-cos y)(1 - sin y)　＜＝[cos2t = 1 - 2sin^2 t => 2sin^2 t = 1 - cos 2t]
= 1 - cos y - sin y + sin y cos y
= 1 - (cos y + sin y) + sin y cos y
= 1 - (-p) + q
= p + q + 1 //