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Question Number 46402 by scientist last updated on 25/Oct/18

$$showthat\cos 7\frac{1}{2}=\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{6}$$

Commented by Meritguide1234 last updated on 25/Oct/18

$$itshouldbecot7\frac{1}{2}$$

Answered by ajfour last updated on 25/Oct/18

$$\cos 15°=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}=\frac{\sqrt{2+\sqrt{3}}}{2}$$$$\cos {\left(\frac{15}{2}\right)}^{°}=\sqrt{\frac{1+\frac{\sqrt{2+\sqrt{3}}}{2}}{2}}$$$$=\frac{\sqrt{2+\sqrt{2+\sqrt{3}}}}{2}.$$

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