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Bisektrissatsen $ \frac{y}{\sqrt{3}/2}=\frac{\frac{1}{2}-y}{1} \Leftrightarrow (2+\sqrt{3})y=\sqrt{3} \Leftrightarrow y = \frac{\sqrt{3}}{2+\sqrt{3}}$ $\sin 15^o=(\frac{\sqrt{3}}{2+\sqrt{3}})/ \sqrt{(\frac{\sqrt{3}}{2+\sqrt{3}})^2 + (\frac{\sqrt{3}}{2})^2} $ $=1/ \sqrt{1 + (\frac{(2+\sqrt{3})\sqrt{3}}{2\sqrt{3}})^2} $ $=2/ \sqrt{4 + (2+\sqrt{3})^2}=2/ \sqrt{11 + 4\sqrt{3}} $
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Sat, 20 May 2023 21:47 GMT