Question

решите уравнение 2cos x/2+1=0

Answer 1

$\displaystyle 2\cos \frac x2+1=0;\qquad 2\cos \frac x2=-1\\\\\cos \frac x2=-\frac12\\\\\frac x2=\pm \arccos \bigg( \! \!-\frac12 \bigg) +2\pi k,k\in \mathbb{Z}\\\\\frac x2=\pm \frac{2\pi}3+2\pi k\; |\cdot 2\qquad k\in \mathbb{Z}\\\\x=\pm \frac{4\pi}3+4\pi k,\;k\in \mathbb{Z}$

Ответ: $\bold {\displaystyle x=\pm \frac{4\pi}3+4\pi k,\; k\in \mathbb{Z}}$