TrigonometryQ2

1) 2cosx ﹣3sinx = 3(cosx + sinx)
2cosx ﹣3sinx = 3cosx + 3sinx
6sinx = - cosx
sinx / cosx = -1 / 6
tanx = -1 / 6
x = 170.5 or 350.5

2) 2cos2 x = sinxcosx
(2cos2 x)2 = sin2xcos2x
4cos4 x = (1﹣cos2x)cos2x
4cos4 x = cos2x ﹣cos4x
5cos4 x ﹣cos2x = 0
cos2x(5cos2x ﹣1) = 0
cos2x = 0 or 5cos2x ﹣1 = 0
cosx = 0 or cos2x = 1 / 5
x = 90,270 or cosx = √(1 / 5) or -√(1 / 5)
x = 90,270 or x = 63.4,116.7,243.4,296.6
∴x = 63.4,90,116.7,243.4,270,296.6

2008-04-20 21:32:52 補充：
唔好意思，第2題不是這麼複雜，應該是
2cos^2 x = sinxcosx
(cosx)(2cosx - sinx)=0
cosx = 0 or 2cosx = sinx
cosx = 0 or tanx = 2
x = 90, 270 or x = 63.4, 243.4
x = 63.4, 90,243.4,270