ctgx>700 inequation

Given the inequality:
$$\cot{\left(x \right)} > 700$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(x \right)} = 700$$
Solve:
Given the equation
$$\cot{\left(x \right)} = 700$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acot}{\left(700 \right)}$$
Or
$$x = \pi n + \operatorname{acot}{\left(700 \right)}$$
, where n - is a integer
$$x_{1} = \pi n + \operatorname{acot}{\left(700 \right)}$$
$$x_{1} = \pi n + \operatorname{acot}{\left(700 \right)}$$
This roots
$$x_{1} = \pi n + \operatorname{acot}{\left(700 \right)}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n + \operatorname{acot}{\left(700 \right)}\right) - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10} + \operatorname{acot}{\left(700 \right)}$$
substitute to the expression
$$\cot{\left(x \right)} > 700$$
$$\cot{\left(\pi n - \frac{1}{10} + \operatorname{acot}{\left(700 \right)} \right)} > 700$$

-cot(1/10 - acot(700)) > 700

Then
$$x < \pi n + \operatorname{acot}{\left(700 \right)}$$
no execute
the solution of our inequality is:
$$x > \pi n + \operatorname{acot}{\left(700 \right)}$$

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