Answer:
x = 60 degrees
or
x = 300 degrees
Step-by-step explanation:
Here, we want to get the exact value of x in degrees
Recall;
sin^2x = 1 - cos^x
Thus, we have that;
2(1 - cos^2x )+ 9cos x - 6 = 0
let cos y = 0
2-2y^2 + 9y -6 = 0
-2y^2 + 9y -4 = 0
-2y^2 + 8y + y - 4 = 0
-2y(y - 4) + 1(y-4) = 0
(1-2y) (y-4) = 0
1 = 2y
y = 4
so y = 1/2 or 4
Since the value of cos cannot be 4, we simply disregard and have y = 1/2 as the only answer
Recall;
y = cos x
cos x = 1/2
x = arc cos 1/2
x = 60 or 300 degrees
