Step-by-step explanation:
½ tan² x − 2 cos² x = 1
tan² x − 4 cos² x = 2
sin² x − 4 cos⁴ x = 2 cos² x
1 − cos² x − 4 cos⁴ x = 2 cos² x
0 = 4 cos⁴ x + 3 cos² x − 1
0 = (cos² x + 1) (4 cos² x − 1)
0 = 4 cos² x − 1
4 cos² x = 1
cos² x = ¼
cos x = ±½
x = π/3, 2π/3, 4π/3, 5π/3
