# trig

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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

• trig -

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

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