Find all solutions of the equation in the interval [0, 2π).

Question

cos(x + 9π) − cos x + 1 = 0

Answer 1

9/2 =4 1/2
so 4 times all the way + one time halfway around which is pi
so you really have cos (x+pi) - cos x + 1 = 0
but cos (a+b) = cos a cos b - sin a sinb
so it is
cos x * (-1) - sin x * (0) - cos x + 1 = 0
-2 cos x = -1
cos x = 0.5
60 and 300 deg