1. The problem statement, all variables and given/known data Hello! Please, let me know if I am heading towards a correct path in solving the equation. I get stuck in the middle, and obviously head away from the result presented in the book. 2. Relevant equations cos(2x) = 2 - 5 cos(x) 3. The attempt at a solution Gather all on one side: cos(2x) - 2 + 5 cos(x) = 0 As cos(2x) = 2 (cos(x))2 - 1 2 (cos(x))2 - 1 - 2 + 5 cos(x) = 0 2 (cos(x))2 + 5 cos(x) - 3 = 0 Let cos(x) = u. Then, 2 u2 + 5 u - 3 = 0 roots of this equation are: u = (- b +- √b2 - 4ac ) / 2a => u = (-5 +- √25 + 24) / 4 = (-5 +- √59) / 4 thus cos(x) = (-5 +- √59) / 4 It is not the end, but I get stuck here because I see that this doesn't seem to lead me to a correct place, because one of the answers is π/3, but if I try to find x from the above expression, I can do it only using arccos( (-5 +- √59) / 4) = x Please, let me know if I am doing something wrong. I have also thought about using Sum to Product formula here, but then I don't get products to work with if I want to set the equation to 0, namely: as cos(α) + cos(β) = 2cos( (α+β)/2) cos( (α-β)/2) But I can't use that sum to product formula in cos(2x) - 2 + 5 cos(x) = 0 because the second cosine has a coefficient 5. Thank you!