sqrt(cos(x)-1)=0 equation

Given the equation
$$\sqrt{\cos{\left(x \right)} - 1} = 0$$
transform
$$\sqrt{\cos{\left(x \right)} - 1} = 0$$
$$\sqrt{\cos{\left(x \right)} - 1} = 0$$
Do replacement
$$w = \cos{\left(x \right)}$$
Given the equation
$$\sqrt{w - 1} = 0$$
so
$$w - 1 = 0$$
Move free summands (without w)
from left part to right part, we given:
$$w = 1$$
We get the answer: w = 1
do backward replacement
$$\cos{\left(x \right)} = w$$
Given the equation
$$\cos{\left(x \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
Or
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, where n - is a integer
substitute w:
$$x_{1} = \pi n + \operatorname{acos}{\left(w_{1} \right)}$$
$$x_{1} = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$x_{1} = \pi n$$
$$x_{2} = \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi$$
$$x_{2} = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
$$x_{2} = \pi n - \pi$$