Question

Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.) 18 + 9 cos(2x) = 27 cos(x)

Answer 1

Using the identity cos(2x) = 2 cos^2x - 1
18 + 9(2 cos^2 x - 1) = 27 cos x
18cos^2 x - 27 cos x + 9 = 0
2 cos^ x - 3 cos x + 1 = 0

(2 cos x  - 1 )(cos x  - 1 ) = 0

cos x = 1/2 , 1 

x =  pi/3, 5pi/3, 0, 2pi     answer