Originally Posted by

**differentiate** Find the exact trigonometric roots of $\displaystyle 16x^5 - 20x^3 + 5x + 1 = 0 $

given that$\displaystyle cos5\theta = 16cos^5\theta - 20cos^3\theta + 5cos\theta$

heres how I did it

let x= cos@

cos5@ = 16x^5 - 20x^3 + 5x + 1

cos5@ = 0, 16x^5 -20x^3 + 5x + 1 = 0

5@ = 2(pi)k +/- pi/2 where k is any integer

= (2(pi)k +/- pi)/10

x = cos@

= cos {2(pi)k +/- pi]/10}

where k is any integer

but how do I proceed to find the five roots of the equation. and is the above correct