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Prove that the three numbers cos40°, cos80° and cos160° have arithmetic mean 0, harmonic mean 1/2 and geometric mean -1/2.
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WHAT?! Nobody has answered this question yet? Shame on you all!
Use the triple-angle formula for cos:
Hence cos40°, cos80° and cos160° are all the distinct roots of the equation 8x[sup]3[/sup] − 6x + 1 = 0.
Now you can answer the question.
Last edited by JaneFairfax (2007-08-11 04:10:43)
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