"\\cos(\\frac{\\pi}{3} + A) = \\cos\\frac{\\pi}{3} \\cos A - \\sin \\frac{\\pi}{3} \\sin A = \\sin\\frac{\\pi}{6} \\cos A - \\cos \\frac{\\pi}{6} \\sin A = \\sin (\\frac{\\pi}{6} - A)" as desired.
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