cos x + cos 2x + cos 3x + cos 4x = 0
更新1:
Ans : x = 36 , 90 , 108 , 180 , 252 , 270 or 324 (degrees) Show your steps clearly.
A.Maths Compound angle
2008-03-01 1:13 am
Solve the following equation for 0 degree < x < 360 degrees
cos x + cos 2x + cos 3x + cos 4x = 0
cos x + cos 2x + cos 3x + cos 4x = 0
回答 (1)
2008-03-01 1:25 am
✔ 最佳答案
cos x + cos 2x + cos 3x + cos 4x = 0 cosx+cos3x+cos2x+cos4x=0
2cos2xcosx+2cos3xcosx=0
cosx(cos2x+cos3x)=0
cosx[2cos(5x/2)cos(x/2)]=0
cosx=0 or cos(5x/2)=0 or cos(x/2)=0
x=90˚,270˚or 5x/2=90˚,270˚,450˚630˚,810˚or x/2= 90˚
x=36˚,90˚,108˚180˚252˚,270˚or 324˚
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