kos^2 theta - sin^2 theta = 0.25

Answer 1

the left side is a well know identity,
cos^2 A - sin^2 A = cos 2A

so we have:

cos 2Ø = 1/4

2Ø = 75.52° or 2Ø = 284.48°
Ø = 37.76° , 142.24°, ...
or
Ø = .659 , 2.4825 ... in radians

general solution in radians:
.659 + kπ/2 , where k is an integer,
2.4825 + kπ/2, where k is an integer.

general solution in degrees:
37.76° + 90k° , 142.24° + 90k°