Cos²x - sin²x = 0,66​

x = 24.35°

Step-by-step explanation:

Recall that

cos²x - sin²x = cos 2x

which means that

cos 2x = 0.66 ---> 2x = cos^-1 (0.66) = 48.7°

or x = 24.35°

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.