[Math] how to calculate the exact value of $\tan \frac{\pi}{10}$

trigonometry

I have an extra homework: to calculate the exact value of $ \tan \frac{\pi}{10}$.
From WolframAlpha calculator I know that it's $\sqrt{1-\frac{2}{\sqrt{5}}} $, but i have no idea how to calculate that.

Thank you in advance,
Greg

Best Answer

look this How to prove $\cos \frac{2\pi }{5}=\frac{-1+\sqrt{5}}{4}$?

then you will get $\sin \frac{\pi}{10}$($\frac{2\pi }{5}+\frac{\pi}{10}=\frac{\pi}{2}$) ,then $\tan \frac{\pi}{10}$.

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