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[sin 3x cos ( \pi/ 3 -4x )+ 1 ]/ [sin (\pi / 3-7x) - cos (\pi / 6+x)+m]=0

Source: 1963-64 Germany R4 12.2

October 12, 2024
trigonometry

Problem Statement

Find all real values xx that satisfy the following equation: sin⁡3xcos(π3−4x)+1sin⁡(π3−7x)−cos(π6+x)+m=0\frac{\sin 3x cos \left(\frac{\pi}{3}-4x \right)+ 1}{\sin \left(\frac{\pi}{3}-7x \right) - cos\left(\frac{\pi}{6}+x \right)+m}= 0 where mm is a given real number.
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