I don't understand the step where 2Sin^2(3pi/10) = 2((sqrt5+1)/4) Attachment 26188

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- December 11th 2012, 01:29 PMEraser147Cos 3pi/5
I don't understand the step where 2Sin^2(3pi/10) = 2((sqrt5+1)/4) Attachment 26188

- December 12th 2012, 01:07 AMchiroRe: Cos 3pi/5
Hey Eraser147.

Try setting up a right angled triangle or using sums or differences formula to get the value. - December 13th 2012, 08:42 AMBobPRe: Cos 3pi/5
Consider the right-angled triangle with acute angles and and note that

To ease typing, let then

Use the standard identities,

and we have the cubic

is a factor, remove this and we are left with the quadratic

and solving this, (for the angle in the range),

Substituting this into (1) and simplifying leads to