solve cos x = -cos 2x for 0 <=x<2pi

Answer 1

Rewrite the equation as cosx +cos2x =0 use the identity that cos²x = ( 1+ cos2x)/2 and solve for cos2x. This gives cos2x= 2cos²x -1 go back to the equation and rewrite as cosx +2cos²x -1 =0. Now use the quadratic formula and solve for cosx this gives cosx = (-1 ±√(1+8))/4 which gives cosx = 1/2, -1 and so x has the values of π/3 and π.