trig
posted by Bob .
To the nearest degree, all of the following angles are solutions of the equation 2sin x + 4 cos 2x =3 except:
(1) 40 degrees
(2) 150 degrees
(3) 166 degrees
(4) 194 degrees

I don't know if you are supposed to do this by simply substiting, or actually solve the equation.
I will solve it
2sinx + 4cos 2x = 3
2sinx + 4(1  2sin^2 x) 3=0
2sinx + 4 8sin^2 x  3 = 0
8sin^2 x  2sinx 1 = 0
sinx = (2 ± √36)/16 = 1/2 or 1/4
x = 30° or 150° or x = 194.4775..° or 345.522°
so to the nearest degree I got
x = 30, 150, 194 and 346
I see only two of these in your list, so the others don't work