Solve sin ( x ) − √ 3 cos ( x ) = − 1 . Give all the solutions in [ 0 , 2 π ) , then all solutions (use k as an arbitrary integer).

Answer 1

sin² x - 2√3 cos x + 3 cos² x = 1

sin² x + cos² x - 2√3 cos x + 2 cos² x = 1

1 - 2√3 cos x + 2 cos² x = 1

- 2√3 cos x + 2 cos² x = 0

2 cos² x - 2√3 cos x = 9

Can you use Zero Product Rule and solve for x?