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

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

Commented by cortano last updated on 19/Oct/21

$$\cos 36°=1-2\sin {}^{2}18°$$$$=1-2{\left(\frac{\sqrt{5}-1}{4}\right)}^2$$$$=1-\left(\frac{6-2\sqrt{5}}{8}\right)$$$$=\frac{2+2\sqrt{5}}{8}=\frac{1+\sqrt{5}}{4}$$

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