1. равенство tg x = 0.

Explanation:

Step1: Recall tangent - function definition

The tangent function is defined as $tgx=\frac{\sin x}{\cos x}$. We want to find when $\frac{\sin x}{\cos x}=0$.

Step2: Determine the condition for the fraction to be zero

A fraction $\frac{a}{b}$ is zero when $a = 0$ and $b\neq0$. For $y = \frac{\sin x}{\cos x}$, we need $\sin x=0$ and $\cos x\neq0$. The solutions of $\sin x = 0$ are $x = k\pi$, where $k\in\mathbb{Z}$. When $x = k\pi$, $\cos(k\pi)=(- 1)^k$. When $k\in\mathbb{Z}$, $\cos(k\pi)\neq0$ for all integer values of $k$.

Answer:

$x = k\pi,k\in\mathbb{Z}$