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Cos2x + 3 = 5cosx


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Use the identity cos(2x)=2(cos(x))^2-1
cos(2x)+3=5cos(x) becomes 2(cos(x))^2-1+3=5cos(x)
Arrange a bit: 2(cos(x))^2-5cos(x)+2=0
Get rid of the 2-factor
(cos(x))^2-(5/2) cos(x)+1=0
This is a quadratic equation for the unknown U=cos(x)
Solve it by factoring or with the quadratic equation formula. The solutions are U=2 or U=1/2.
Since U=cos(x), the root U=cox(x)=2 must be rejected.
What is left is cos(x)=(1/2). The solutions are x=60 or x=-60 plus or minus 360 degrees.

Posted on Jul 26, 2014


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Cos2x + 3 = 5cosx

the solution you got is correct it is

cos X =2 and cos X =1/2

but we know maximum value of cosX is we discard the solution cos X =2

so only solution is cos X=1/2

and X = 60 degrees

hope you r satisfied.please rate the solution high.thank you

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