Question 86730: please help me solve this equation: cos 4x=sin2x from 0 to 360 degress.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve this equation: cos 4x=sin2x from 0 to 360 degrees
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cos(4x) = cos^2(2x)-sin^2(2x)
cos^2(2x) = 1-sin^2(2x)
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Therefore your equation can be written:
cos^2(2x)-sin^2(2x)=sin2x
[1-sin^2(2x)] - sin^2(2x) = sin(2x)
2sin^2(2x)+sin(2x)-1=0
(2sin(2x)-1)(sin(2x)+1)=0
2sin(2x)=1 or sin(2x)=-1
sin(2x)=1/2 or sin(2x)=-1
2x=30 degrees or 150 degrees; 2x= 210 degrees or 330 degrees
x=15 degrees or 75 degrees; x=105 degrees or 165 degrees
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If the restricion "from 0 to 360" refers to the x value,
there are addtional solutions. I have made the assumption
the restriction refers to 2x.
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Cheers,
stan H.
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