Find the general solution of 4 cos 2x - 4 sqr | vedclass

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(C) Given equation: $4 \cos 2x - 4 \sqrt{3} \sin 2x + \cos 3x - \sqrt{3} \sin 3x + \cos x - \sqrt{3} \sin x = 0$ Grouping terms: $4(\cos 2x - \sqrt{3}

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$\frac{n \pi}{2} + \frac{\pi}{12}$

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(C) Given equation: $4 \cos 2x - 4 \sqrt{3} \sin 2x + \cos 3x - \sqrt{3} \sin 3x + \cos x - \sqrt{3} \sin x = 0$ Grouping terms: $4(\cos 2x - \sqrt{3} \sin 2x) + (\cos 3x + \cos x) - \sqrt{3}(\sin 3x + \sin x) = 0$ Using sum-to-product formulas: $4(\cos 2x - \sqrt{3} \sin 2x) + 2 \cos 2x \cos x - 2 \sqrt{3} \sin 2x \cos x = 0$ Factoring out common terms: $2(\cos 2x - \sqrt{3} \sin 2x)(2 + \cos x) = 0$ Since $2 + \cos x 
eq 0$ for all real $x$,we have $\cos 2x - \sqrt{3} \sin 2x = 0$ $\Rightarrow \cos 2x = \sqrt{3} \sin 2x$ $\Rightarrow 	an 2x = \frac{1}{\sqrt{3}}$ $\Rightarrow 2x = n \pi + \frac{\pi}{6}$ $\Rightarrow x = \frac{n \pi}{2} + \frac{\pi}{12}$

Find the general solution of $4 \cos 2x - 4 \sqrt{3} \sin 2x + \cos 3x - \sqrt{3} \sin 3x + \cos x - \sqrt{3} \sin x = 0$.

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