If the image of the function y = ACOS (x − π 6) sin (ω x + π 6) (a > 0, ω > 0) is shifted to the left by π 6 units, the image obtained is symmetrical about the origin, then the value of ω may be () A. 2B. 3C. 4D. 5

Because y = ACOS (x − π 6) sin (ω x + π 6) (a > 0, ω > 0) when the image is shifted to the left by π 6 units, the resulting function is y = acosxsin [ω (x + π 6) + π 6] (a > 0, ω > 0) for a, the translated function is y = acosxsin (2x + π 2) = - acosxx, which is even and not symmetric about the origin

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