show that x = cos(π/10) is a root of the equation 16x^4 - 20x^2 + 5 = 0.

proof:

let y =  π/10

we have

 cos5y = 16cos^5 y - 20cos^3 y + 5cosy

or 0 =  16cos^5 y - 20cos^3 y + 5cosy

= (16cos^4 y - 20cos^2 y + 5)cos y

as cos  y is not zero 

 so (16cos^4 y - 20cos^2 y + 5) = 0

hence x =  cos(π/10) is a root