Answer:
x = 24.35, 155.65, 204.35, 335.65 degrees ( for 0 < x < 360 degrees).
Step-by-step explanation:
cos²x - sin²x = 0.66
cos^2 x = 1 - sin^2 x so
1 - sin^2 x - sin^2 x = 0.66
1 - 2sin^2 x = 0.66
2sin^2 x = 1 - 0.66
sin^2x = 0.34/2 = 0.17
sin x = +/- √0.17
= +/- 0.41231
x = 24.35 degrees ( in first quadrant)
and 180 + 24.35 = 204.35 degrees in third quadrant.
