Answer:
x = pi/12, 5pi/12, 13pi/12, 17pi/12.
Step-by-step explanation:
Note that cos (4x) = 1 - 2sin^2 (2x)
Substituting we have:
1 - 2sin^2 (2x) - 9 sin(2x) + 4 = 0
2 sin^2 (2x) + 9 sin(2x) - 5 = 0
(2 sin 2x - 1 )(sin 2x + 5 ) = 0
sin 2x = 1/2 and sin 2x = -5.
sin 2x = 1/2, gives 2x = pi/6, 5pi/6, 13pi/6, 17pi/6.
There are no solutions to sin 2x = -5 because the range of sin x is -1 to +1.
So x = pi/12, 5pi/12, 13pi/12, 17pi/12.
