1.已知sina,cosa为方程2x的平方+(根号3-1)x+m=0的两个不等根,其中0

Question

1.已知sina,cosa为方程2x的平方+(根号3-1)x+m=0的两个不等根,其中0

Answer 1

1,
2x^2 + (3^(1/2) - 1)x + m = 0,
cosasina = m/2,m = sin(2a).
cosa + sina = (1 - 3^(1/2))/2,
sina = 1/2,cosa = -3^(1/2)/2,a = 5PI/6,
m = sin(5PI/3) = -3^(1/2)/2
tana = -3^(-1/2)
cota = -3^(1/2)
tana - cota = 3^(1/2) - 3^(-1/2) = 2/3^(1/2)
2,
sina = 2cosa,
(sina)^2 = 4(cosa)^2 = 4 - 4(sina)^2,
(sina)^2 = 4/5
3(sina)^2 - 2sinacosa = 3(sina)^2 - (sina)^2 = 2(sina)^2
= 2*4/5 = 8/5