Find the solution(s) of the equation in the interval [0, 2𝜋). Use a graphing utility to verify your results. (Enter your answers as a comma-separated list.)

Question

3cos(x + 5𝜋/6) - 3cos(x - 5𝜋/6) = 3

x = _________

Answer 1

cos(x + 5π/6) - cos(x - 5π/6) = 1

[cosxcos(5π/6) - sinxsin(5π/6)] - [cosxcos(5π/6) + sinxsin(5π/6)] = 1

-2sinxsin(5π/6) = 1

-2sinx(1/2) = 1

sinx = -1

x = 3π/2

Answer 2

cos (x + 5π/6) - cos (x - 5π/6 = 1

cos x cos 5π/6 - sin x sin 5π/6 - (cos x cos 5ππ6 - sin x sin 5π/6) = 1

cos x cos 5π/6 - sin x sin 5π/6 - cos x cos 5ππ6 + sin x sin 5π/6 = 1

0 = 1

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