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How would I get the exact value of Tan157.5 using the half angle formula?

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Hippalectryonidn
[tex]\tan(157.5)=\tan(315/2)=\frac{\sin(315)}{1+\cos(315)}=\frac{-\sqrt{2}/2}{1+\sqrt{2}/2}=\frac{-1}{1+\sqrt{2}}[/tex]
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