Question

solve cos^4-1=0 for all real values of x.

Answer 1

factorize it, first
cos^4 x - 1 = 0
(cos^2 x + 1)(cos^2 x - 1) = 0
(cos^2 x + 1)(cosx + 1)(cosx - 1) = 0
set up each factor to equal zero, then solve for x

(notice : cos^2 x + 1 = 0, it has no real solution for x)