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# Any idea why this is wrong / Trig

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Veteran  Mar 21, 2017
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I'll do the first on and you can try the others yourself

$$cos(u)=\frac{\sqrt{15}}{5}\\ cos(2*\frac{u}{2})=\frac{\sqrt{15}}{5}\\ cos^2(\frac{u}{2})-sin^2(\frac{u}{2})=\frac{\sqrt{15}}{5}\\ 1-sin^2(\frac{u}{2})-sin^2(\frac{u}{2})=\frac{\sqrt{15}}{5}\\ 1-2sin^2(\frac{u}{2})=\frac{\sqrt{15}}{5}\\ -2sin^2(\frac{u}{2})=\frac{\sqrt{15}-5}{5}\\ sin^2(\frac{u}{2})=\frac{\sqrt{15}-5}{-10}\\ sin^2(\frac{u}{2})=\frac{5-\sqrt{15}}{10}\\ sin(\frac{u}{2})=\sqrt{\frac{5-\sqrt{15}}{10}}\\ sin(\frac{u}{2})=\frac{\sqrt{(5-\sqrt{15})}}{\sqrt{10}}\times \frac{\sqrt{10}}{\sqrt{10}}\\ sin(\frac{u}{2})=\frac{\sqrt{10(5-\sqrt{15})}}{10}\\ sin(\frac{u}{2})=\frac{\sqrt{50-10\sqrt{15}}}{10}\\$$

Melody  Mar 21, 2017