Use $\cos 5\theta$ to find the roots of $x(16x^4 - 20x^2 + 5) = 0$ I used $\cos(3\theta + 2\theta)$ to prove the first part, but I don't know how to the $2$nd part.
Show that $\cos 5\theta=16\cos^5\theta-20\cos^3\theta+5\cos\theta,$ and hence show that
$$\text{the roots of }x(16x^4 - 20x^2 + 5) \text{ are: } 0,\cos\frac{\pi}{10}, \cos\frac{3\pi}{10},\cos\frac{7\pi}{10}, \cos\frac{9\pi}{10}$$


Here the value of cosine will repeat after point.
Final values wil be only 5
