Prove-that-cos20-1-3-cos80-1-3-cos160-1-3-3-9-1-3-6-2-1-3-

Question Number 217857 by hardmath last updated on 22/Mar/25

Prove that :

\sqrt[3]{\cos 20 °} + \sqrt[3]{\cos 80 °} + \sqrt[3]{\cos 160 °} = \sqrt[3]{\frac{3 \cdot \sqrt[3]{9} - 6}{2}}

Answered by Frix last updated on 22/Mar/25

Staying in R \Rightarrow \sqrt[3]{\cos 20 °} = - \sqrt[3]{\cos 160 °} \Rightarrow

\cos 80 ° = \frac{3}{2} \sqrt[3]{9} - 3 \approx . 12

But \cos 80 ° \approx . 17

\Rightarrow false claim

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