Question

Математика розв'язати
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Answer 1

$3\mathrm{tg}3x=-\sqrt{3}\Leftrightarrow \mathrm{tg}3x=-\cfrac{1}{\sqrt{3}}\Rightarrow 3x=-\cfrac{\pi}{6}+\pi k,k\in \mathbb{Z}\Rightarrow x=-\cfrac{\pi}{18}+\cfrac{\pi k}{3},k\in \mathbb{Z}$

$\cos\left(x+\cfrac{\pi}{3}\right)+\cos\left(x-\cfrac{\pi}{3}\right)=\dfrac{1}{2}\Leftrightarrow 2\cos\left ( \cfrac{1}{2}\left ( x+\cfrac{\pi}{3}+x-\cfrac{\pi}{3} \right ) \right )\cos\left ( \cfrac{1}{2}\left ( x+\cfrac{\pi}{3}-x+\cfrac{\pi}{3} \right ) \right )=\cfrac{1}{2} \cos x=\cfrac{1}{2}\Rightarrow x=\pm \cfrac{\pi}{3}+2\pi k,k\in \mathbb{Z}$