mathz f.4 m2

tanA+cotA
= sinA/cosA + cosA/sinA
= [(sinA)^2 + (cosA)^2] / (sinA cosA)
= 1 / (sinA cosA)
= 2 / (2 sinA cosA)
= 2 / sin2A
;

x^2+(tanA+cotA)x+1 = 0
x^2 + (2/sin2A)x + 1 = 0
Since 2-√3 is one of the roots ,
the other root = 1 / (2 - √3) = 2 + √3
Sum of the roots = - 2/sin2A = 2 - √3 + 2 + √3 = 4
sin2A = - 1/2 , (2A = 330°)
So
(cos2A)^2 = 1 - (sin2A)^2 = 1 - 1/4 = 3/4
cos2A = √3/2 or - √3/2(rejected)


or

cos2A = cos330° = √3/2




2010-05-28 01:58:43 補充：
Missing something ,

When 2A = 210° ,

cos2A = cos 210° = - √3/2