I am trying to prove that cos(pi/5)= (1+sqrt(5))/4
I tried finding the 5th roots of unity and then just using the real part cis(pi/5) but then i dont know how to get it = (1+sqrt(5))/4.
I am stuck somewhere here.
Hello kayla09
nzmathman has shown you how to find $\displaystyle \sin \pi/5$. Now use
$\displaystyle \cos^2(\pi/5) = 1 - \sin^2(\pi/5)$
$\displaystyle = 1 - \frac{5-\sqrt 5}{8}$
$\displaystyle = \frac{3+\sqrt 5}{8}$
$\displaystyle = \frac{6+2\sqrt 5}{16}$
$\displaystyle = \frac{1+2\sqrt 5+5}{16}$
$\displaystyle = \frac{(1+\sqrt 5)^2}{4^2}$
$\displaystyle \Rightarrow \cos(\pi/5) =\frac{1+\sqrt 5}{4}$, taking the positive square root.
Grandad