compound angles

cos(x+15*) cos(x-15*) - sinx sin(x-30*) = cos165*
(1/2)cos2x + (1/2)cos30* - (1/2)cos30* + (1/2)cos(2x-30*)=cos 165*
cos 2x + cos (2x-30*) = 2 cos 165*
2 cos (2x-15*) cos 15* = -2 cos 15*
cos ( 2x - 15* ) = -1
2x - 15* = 180*
2x = 195*
x = 97.5*

2008-04-11 11:11:31 補充：
Sorry for missing one root:
2x - 15* = 180*, 540*
2x = 195* or 555*
x = 97.5* or 277.5*

cos(x+15) cos(x-15) - sinx sin(x-30) = cos165
1/2[cos2x+cos30]+1/2[cos(2x-30)-cos30] = cos(180-15)
1/2[cos2x+cos(2x-30)] = -cos15
cos(2x-15)cos15 = -cos15
cos(2x-15) = -1
2x-15 = 180, 540
x = 97.5, 277.5