Let f (x) = sin (Wx + 2 π / 3) + sin (wx-2 π / 3) (W > 0) have the minimum positive period of π, and find the monotone interval of the function?
F (x) = sin (Wx + 2 π / 3) + sin (wx-2 π / 3) = sinwxcos (2 π / 3) + coswxsin (2 π / 3) + sinwxcos (2 π / 3) - coswxsin (2 π / 3) = sinwxcos (2 π / 3) + sinwxcos (2 π / 3) = 2sinwxcos (2 π / 3) = - sinwx ∵ t = π∵ 2 π / w = π w = 2 ∵ the function is a simple function of F (x) = sin2x ∵
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