Answer:
x = pi/2, 3pi/2 x = pi
Explanation:
cos2x + 2 cos x + 1 = 0
cos 2x = cos^2 - sin^2x trig identity
cos^2x -sin^2 + 2cos x +1 = 0
rearrange
cos^2 x +2cos x + 1-sin^2 x = 0
1 - sin^2 x = cos^2 x trig identity
cos^2 x + 2 cos x + cos ^2 x = 0
combine like terms
2 cos ^2 x + 2 cos x = 0
divide by 2
cos ^2 x + cos x = 0
factor out a cos x
cos (x) (cos x +1) = 0
using the zero product property
cos (x) = 0 cos x + 1 =0
cos x =0 cos x = -1
taking the arccos of each side
arccos cos x = arccos (0) arccos (cos x) = arccos (-1)
x = pi/2, 3pi/2 x = pi