Упростите выражение: 6 sin(2x-pi/6)cos(3x+pi/3)-3sin(5x+pi/6)

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6sin(2x-π/6)cos(3x+π/3) - 3sin(5x+π/6)
= 6[sin(2x)cos(π/6) - cos(2x)sin(π/6)][cos(3x)cos(π/3)-sin(3x)sin(π/3)] - 3sin(5x+π/6)
= 6[sin(2x)cos(π/6) - cos(2x)sin(π/6)][cos(3x)cos(π/3)-sin(3x)sin(π/3)] - 3[sin(5x)cos(π/6) + cos(5x)sin(π/6)]
= 6[sin(2x)cos(π/6) - cos(2x)sin(π/6)][cos(3x)cos(π/3)-sin(3x)sin(π/3)] - 3[sin(5x)cos(π/6) + cos(5x)sin(π/6)]
= 6[sin(2x)cos(π/6) - cos(2x)sin(π/6)][cos(3x)cos(π/3)-sin(3x)sin(π/3)] - 3[sin(5x)cos(π/6) + cos(5x)sin(π/6)]

You can continue simplifying it further based on trigonometric identities.