Trigonometry question help?

Question

Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0,2π). Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution."

2cos2(x)+4cos(x)=6

Enter your answer in radians, as an exact answer when possible. Multiple solutions should be separated by commas.

Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used.

X=

Answer 1

This problem is trivial to solve. cos x and cos 2x have maximum values of 1, and both are required in order for

2 cos 2x + 4 cos x = 6

cos x = 1 only once on [0, 2 pi), at 0, and cos 2x = 1 there as well.

Thus, the only solution on [0, 2pi) is 0.

Even if the first term was (cos (x))^2, we would have the same result.