Question

4cos3x*ctgx=0 найти корень

Answer 1

$4\cos (3x)\cot x=0\\\\ 4\cos 3x=0\\ \cos 3x=0\\ 3x=\dfrac{\pi}{2}+k\pi\\ x=\dfrac{\pi}{6}+\dfrac{k\pi}{3}\\\\ \cot x=0\\ x=\dfrac{\pi}{2}+k\pi\\\\ \boxed{x=\left\{\dfrac{\pi}{6}+\dfrac{k\pi}{3},\dfrac{\pi}{2}+k\pi,(k\in\mathbb{Z})\right\}}$