tgx>2 inequation

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tan(x) > 2

\tan{\left(x \right)} > 2

tan(x) > 2

Detail solution

Given the inequality:

\tan{\left(x \right)} > 2

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

\tan{\left(x \right)} = 2

Solve:
Given the equation

\tan{\left(x \right)} = 2

- this is the simplest trigonometric equation
This equation is transformed to

x = \pi n + \operatorname{atan}{\left(2 \right)}

Or

x = \pi n + \operatorname{atan}{\left(2 \right)}

, where n - is a integer

x_{1} = \pi n + \operatorname{atan}{\left(2 \right)}

x_{1} = \pi n + \operatorname{atan}{\left(2 \right)}

This roots

x_{1} = \pi n + \operatorname{atan}{\left(2 \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{atan}{\left(2 \right)}\right) + - \frac{1}{10}

=

\pi n - \frac{1}{10} + \operatorname{atan}{\left(2 \right)}

substitute to the expression

\tan{\left(x \right)} > 2

\tan{\left(\pi n - \frac{1}{10} + \operatorname{atan}{\left(2 \right)} \right)} > 2

tan(-1/10 + pi*n + atan(2)) > 2

Then

x < \pi n + \operatorname{atan}{\left(2 \right)}

no execute
the solution of our inequality is:

x > \pi n + \operatorname{atan}{\left(2 \right)}

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       x1

Solving inequality on a graph

Rapid solution [src]

   /    pi             \
And|x < --, atan(2) < x|
   \    2              /

x < \frac{\pi}{2} \wedge \operatorname{atan}{\left(2 \right)} < x

(atan(2) < x)∧(x < pi/2)

Rapid solution 2 [src]

          pi 
(atan(2), --)
          2

x\ in\ \left(\operatorname{atan}{\left(2 \right)}, \frac{\pi}{2}\right)

x in Interval.open(atan(2), pi/2)