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xax
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I've started to work on the it, just tell me if I'm on the right track.
cos (45-30) = ([tex]\sqrt{3}[/tex] + 1) / 2[tex]\sqrt{2}[/tex] so cos 15 is irrational.
cos3x = 4cos^3x - 3cos x [tex]\Rightarrow[/tex] cos 5 is irrational
cos 4x... cos 20
If this is a bad way, maybe someone knows a better one.
Here is what I think a better way:
cos3x = 4cos^3x - 3cosx so cos20 is the solution for 8x^3 - 6x - 1 and this one has no rational solutions so cos20 is irrational
cos (45-30) = ([tex]\sqrt{3}[/tex] + 1) / 2[tex]\sqrt{2}[/tex] so cos 15 is irrational.
cos3x = 4cos^3x - 3cos x [tex]\Rightarrow[/tex] cos 5 is irrational
cos 4x... cos 20
If this is a bad way, maybe someone knows a better one.
Here is what I think a better way:
cos3x = 4cos^3x - 3cosx so cos20 is the solution for 8x^3 - 6x - 1 and this one has no rational solutions so cos20 is irrational
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