F4 a-math

As follows:

圖片參考：http://i238.photobucket.com/albums/ff245/chocolate328154/Maths169.jpg?t=1203172047


2008-02-17 00:46:56 補充：
唔好意思, 頭先跳咗d steps, e+加返上去la, 請禁reload。

sin(30˚-x)cos(30˚+x)=√3/2
1/2[sin[(30˚-x)+(30˚+x)]+sin[(30˚-x)-(30˚+x)]=)=√3/2
sin60˚-sin2x=√3
√3/2-sin2x=√3
sin2x=-√3/2
2x=60˚,120˚,420˚或480˚
x=30˚,60˚,210˚或240˚

2008-02-17 13:27:41 補充：
sin2x=-√3/22x=240˚,300˚,600˚或660˚x=120˚,150˚,300˚或330˚

Let 30-x=A and 30+x=B
Then sinAcosB = (sin(A+B) + sin(A-B))/2

sin(30-x)cos(30+x) =(sin(30-x+30+x) + sin(30-x-30-x))/2 =(sin60 + sin(-2x))/2
=((3)^(1/2)/2 - sin2x)/2

therefore ((3)^(1/2)/2 - sin2x)/2 = (3)^(1/2)/2=======> (3)^(1/2)/2 - sin2x) = (3)^(1/2)

sin2x = - (3)^(1/2)/2

Since 0˚≤X≤360˚ therefor 0˚≤2X≤720˚

2x = 180+60, 360-60, 540 + 60 or 720-60

2x = 240, 300, 600 or 660

or x = 120, 150, 300 or 330