prove-that-cos-36-1-5-4-

Question Number 157065 by apriadodir last updated on 19/Oct/21

prove that \cos 36 ° = \frac{1 + \sqrt{5}}{4}

Commented by cortano last updated on 19/Oct/21

\cos 36 ° = 1 - 2 \sin^{2} 18 °

= 1 - 2 {(\frac{\sqrt{5} - 1}{4})}^{2}

= 1 - (\frac{6 - 2 \sqrt{5}}{8})

= \frac{2 + 2 \sqrt{5}}{8} = \frac{1 + \sqrt{5}}{4}

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