I have an exercise as follows:

Show that: cos(5*angle)=16*cos^5(angle)-20*cos^3(angle)+cos(angle), and hence show that the roots of: x(16x^4-20x^2+5)=0 are 0; cos(pi/10); cos(3*pi/10); cos(7*pi/10) and cos(9*pi/10)

The first part has me completely confused, but the second part is also confusing.

Could you show me what way to do this?

thx