ctg(x)<=1 inequation

You have entered [src]

cot(x) <= 1

\cot{\left(x \right)} \leq 1

cot(x) <= 1

Detail solution

Given the inequality:

\cot{\left(x \right)} \leq 1

To solve this inequality, we must first solve the corresponding equation:

\cot{\left(x \right)} = 1

Solve:
Given the equation

\cot{\left(x \right)} = 1

transform

\cot{\left(x \right)} - 1 = 0

\cot{\left(x \right)} - 1 = 0

Do replacement

w = \cot{\left(x \right)}

Move free summands (without w)
from left part to right part, we given:

w = 1

We get the answer: w = 1
do backward replacement

\cot{\left(x \right)} = w

substitute w:

x_{1} = \frac{\pi}{4}

x_{1} = \frac{\pi}{4}

This roots

x_{1} = \frac{\pi}{4}

is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:

x_{0} \leq x_{1}

For example, let's take the point

x_{0} = x_{1} - \frac{1}{10}

=

- \frac{1}{10} + \frac{\pi}{4}

=

- \frac{1}{10} + \frac{\pi}{4}

substitute to the expression

\cot{\left(x \right)} \leq 1

\cot{\left(- \frac{1}{10} + \frac{\pi}{4} \right)} \leq 1

   /1    pi\     
tan|-- + --| <= 1
   \10   4 /

but

   /1    pi\     
tan|-- + --| >= 1
   \10   4 /

Then

x \leq \frac{\pi}{4}

no execute
the solution of our inequality is:

x \geq \frac{\pi}{4}

         _____  
        /
-------•-------
       x1

Rapid solution [src]

   /pi             \
And|-- <= x, x < pi|
   \4              /

\frac{\pi}{4} \leq x \wedge x < \pi

(x < pi)∧(pi/4 <= x)

Rapid solution 2 [src]

 pi     
[--, pi)
 4

x\ in\ \left[\frac{\pi}{4}, \pi\right)

x in Interval.Ropen(pi/4, pi)