Mister Exam
|tgt|>2 inequation
The solution
Detail solution
Given the inequality:
$$\left|{\tan{\left(t \right)}}\right| > 2$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{\tan{\left(t \right)}}\right| = 2$$
Solve:
Given the equation
$$\left|{\tan{\left(t \right)}}\right| = 2$$
transform
$$\left|{\tan{\left(t \right)}}\right| - 2 = 0$$
$$\left|{\tan{\left(t \right)}}\right| - 2 = 0$$
Do replacement
$$w = \left|{\tan{\left(t \right)}}\right|$$
Move free summands (without w)
from left part to right part, we given:
$$w = 2$$
We get the answer: w = 2
do backward replacement
$$\left|{\tan{\left(t \right)}}\right| = w$$
substitute w:
$$x_{1} = 39.7335557788732$$
$$x_{2} = 30.3087778181038$$
$$x_{3} = -11.4592218965651$$
$$x_{4} = -54.5142238288206$$
$$x_{5} = 83.7158529291303$$
$$x_{6} = -49.1583337396426$$
$$x_{7} = 85.9301503647185$$
$$x_{8} = 26.2398899465124$$
$$x_{9} = 77.4326676219507$$
$$x_{10} = 10.5319266785635$$
$$x_{11} = 8.31762924297529$$
$$x_{12} = 89.9990382363099$$
$$x_{13} = -41.9478532144614$$
$$x_{14} = -26.2398899465124$$
$$x_{15} = 48.231038521641$$
$$x_{16} = 17.7424072037447$$
$$x_{17} = -13.6735193321533$$
$$x_{18} = -33.4503704716936$$
$$x_{19} = -8.31762924297529$$
$$x_{20} = 82.7885577111287$$
$$x_{21} = -32.523075253692$$
$$x_{22} = -5.1760365893855$$
$$x_{23} = 2.0344439357957$$
$$x_{24} = -17.7424072037447$$
$$x_{25} = 11.4592218965651$$
$$x_{26} = 4.24874137138388$$
$$x_{27} = -89.9990382363099$$
$$x_{28} = -74.2910749683609$$
$$x_{29} = -4.24874137138388$$
$$x_{30} = 38.8062605608716$$
$$x_{31} = 68.0078896611814$$
$$x_{32} = -48.231038521641$$
$$x_{33} = 32.523075253692$$
$$x_{34} = 63.93900178959$$
$$x_{35} = 74.2910749683609$$
$$x_{36} = -71.1494823147711$$
$$x_{37} = -55.4415190468222$$
$$x_{38} = -70.2221870967695$$
$$x_{39} = 46.0167410860528$$
$$x_{40} = 80.5742602755405$$
$$x_{41} = 33.4503704716936$$
$$x_{42} = 55.4415190468222$$
$$x_{43} = -85.9301503647185$$
$$x_{44} = -27.167185164514$$
$$x_{45} = -83.7158529291303$$
$$x_{46} = -10.5319266785635$$
$$x_{47} = 61.7247043540018$$
$$x_{48} = 54.5142238288206$$
$$x_{49} = 13.6735193321533$$
$$x_{50} = -39.7335557788732$$
$$x_{51} = -96.2822235434895$$
$$x_{52} = -143.406113347336$$
$$x_{53} = -77.4326676219507$$
$$x_{54} = -35.6646679072818$$
$$x_{55} = -52.2999263932324$$
$$x_{56} = -98.4965209790777$$
$$x_{57} = 76.5053724039491$$
$$x_{58} = 98.4965209790777$$
$$x_{59} = 19.9567046393328$$
$$x_{60} = -68.0078896611814$$
$$x_{61} = 96.2822235434895$$
$$x_{62} = -63.93900178959$$
$$x_{63} = -30.3087778181038$$
$$x_{64} = 24.0255925109243$$
$$x_{65} = -24.0255925109243$$
$$x_{66} = 60.7974091360002$$
$$x_{67} = 16.8151119857431$$
$$x_{68} = 99.4238161970793$$
$$x_{69} = 52.2999263932324$$
$$x_{70} = -46.0167410860528$$
$$x_{71} = -99.4238161970793$$
$$x_{72} = 92.2133356718981$$
$$x_{73} = 41.9478532144614$$
$$x_{74} = 70.2221870967695$$
$$x_{75} = -61.7247043540018$$
$$x_{76} = -57.6558164824104$$
$$x_{77} = -92.2133356718981$$
$$x_{78} = -2.0344439357957$$
$$x_{79} = -93.1406308898997$$
$$x_{80} = -19.9567046393328$$
$$x_{81} = -76.5053724039491$$
$$x_{82} = -79.6469650575389$$
$$x_{1} = 39.7335557788732$$
$$x_{2} = 30.3087778181038$$
$$x_{3} = -11.4592218965651$$
$$x_{4} = -54.5142238288206$$
$$x_{5} = 83.7158529291303$$
$$x_{6} = -49.1583337396426$$
$$x_{7} = 85.9301503647185$$
$$x_{8} = 26.2398899465124$$
$$x_{9} = 77.4326676219507$$
$$x_{10} = 10.5319266785635$$
$$x_{11} = 8.31762924297529$$
$$x_{12} = 89.9990382363099$$
$$x_{13} = -41.9478532144614$$
$$x_{14} = -26.2398899465124$$
$$x_{15} = 48.231038521641$$
$$x_{16} = 17.7424072037447$$
$$x_{17} = -13.6735193321533$$
$$x_{18} = -33.4503704716936$$
$$x_{19} = -8.31762924297529$$
$$x_{20} = 82.7885577111287$$
$$x_{21} = -32.523075253692$$
$$x_{22} = -5.1760365893855$$
$$x_{23} = 2.0344439357957$$
$$x_{24} = -17.7424072037447$$
$$x_{25} = 11.4592218965651$$
$$x_{26} = 4.24874137138388$$
$$x_{27} = -89.9990382363099$$
$$x_{28} = -74.2910749683609$$
$$x_{29} = -4.24874137138388$$
$$x_{30} = 38.8062605608716$$
$$x_{31} = 68.0078896611814$$
$$x_{32} = -48.231038521641$$
$$x_{33} = 32.523075253692$$
$$x_{34} = 63.93900178959$$
$$x_{35} = 74.2910749683609$$
$$x_{36} = -71.1494823147711$$
$$x_{37} = -55.4415190468222$$
$$x_{38} = -70.2221870967695$$
$$x_{39} = 46.0167410860528$$
$$x_{40} = 80.5742602755405$$
$$x_{41} = 33.4503704716936$$
$$x_{42} = 55.4415190468222$$
$$x_{43} = -85.9301503647185$$
$$x_{44} = -27.167185164514$$
$$x_{45} = -83.7158529291303$$
$$x_{46} = -10.5319266785635$$
$$x_{47} = 61.7247043540018$$
$$x_{48} = 54.5142238288206$$
$$x_{49} = 13.6735193321533$$
$$x_{50} = -39.7335557788732$$
$$x_{51} = -96.2822235434895$$
$$x_{52} = -143.406113347336$$
$$x_{53} = -77.4326676219507$$
$$x_{54} = -35.6646679072818$$
$$x_{55} = -52.2999263932324$$
$$x_{56} = -98.4965209790777$$
$$x_{57} = 76.5053724039491$$
$$x_{58} = 98.4965209790777$$
$$x_{59} = 19.9567046393328$$
$$x_{60} = -68.0078896611814$$
$$x_{61} = 96.2822235434895$$
$$x_{62} = -63.93900178959$$
$$x_{63} = -30.3087778181038$$
$$x_{64} = 24.0255925109243$$
$$x_{65} = -24.0255925109243$$
$$x_{66} = 60.7974091360002$$
$$x_{67} = 16.8151119857431$$
$$x_{68} = 99.4238161970793$$
$$x_{69} = 52.2999263932324$$
$$x_{70} = -46.0167410860528$$
$$x_{71} = -99.4238161970793$$
$$x_{72} = 92.2133356718981$$
$$x_{73} = 41.9478532144614$$
$$x_{74} = 70.2221870967695$$
$$x_{75} = -61.7247043540018$$
$$x_{76} = -57.6558164824104$$
$$x_{77} = -92.2133356718981$$
$$x_{78} = -2.0344439357957$$
$$x_{79} = -93.1406308898997$$
$$x_{80} = -19.9567046393328$$
$$x_{81} = -76.5053724039491$$
$$x_{82} = -79.6469650575389$$
This roots
$$x_{52} = -143.406113347336$$
$$x_{71} = -99.4238161970793$$
$$x_{56} = -98.4965209790777$$
$$x_{51} = -96.2822235434895$$
$$x_{79} = -93.1406308898997$$
$$x_{77} = -92.2133356718981$$
$$x_{27} = -89.9990382363099$$
$$x_{43} = -85.9301503647185$$
$$x_{45} = -83.7158529291303$$
$$x_{82} = -79.6469650575389$$
$$x_{53} = -77.4326676219507$$
$$x_{81} = -76.5053724039491$$
$$x_{28} = -74.2910749683609$$
$$x_{36} = -71.1494823147711$$
$$x_{38} = -70.2221870967695$$
$$x_{60} = -68.0078896611814$$
$$x_{62} = -63.93900178959$$
$$x_{75} = -61.7247043540018$$
$$x_{76} = -57.6558164824104$$
$$x_{37} = -55.4415190468222$$
$$x_{4} = -54.5142238288206$$
$$x_{55} = -52.2999263932324$$
$$x_{6} = -49.1583337396426$$
$$x_{32} = -48.231038521641$$
$$x_{70} = -46.0167410860528$$
$$x_{13} = -41.9478532144614$$
$$x_{50} = -39.7335557788732$$
$$x_{54} = -35.6646679072818$$
$$x_{18} = -33.4503704716936$$
$$x_{21} = -32.523075253692$$
$$x_{63} = -30.3087778181038$$
$$x_{44} = -27.167185164514$$
$$x_{14} = -26.2398899465124$$
$$x_{65} = -24.0255925109243$$
$$x_{80} = -19.9567046393328$$
$$x_{24} = -17.7424072037447$$
$$x_{17} = -13.6735193321533$$
$$x_{3} = -11.4592218965651$$
$$x_{46} = -10.5319266785635$$
$$x_{19} = -8.31762924297529$$
$$x_{22} = -5.1760365893855$$
$$x_{29} = -4.24874137138388$$
$$x_{78} = -2.0344439357957$$
$$x_{23} = 2.0344439357957$$
$$x_{26} = 4.24874137138388$$
$$x_{11} = 8.31762924297529$$
$$x_{10} = 10.5319266785635$$
$$x_{25} = 11.4592218965651$$
$$x_{49} = 13.6735193321533$$
$$x_{67} = 16.8151119857431$$
$$x_{16} = 17.7424072037447$$
$$x_{59} = 19.9567046393328$$
$$x_{64} = 24.0255925109243$$
$$x_{8} = 26.2398899465124$$
$$x_{2} = 30.3087778181038$$
$$x_{33} = 32.523075253692$$
$$x_{41} = 33.4503704716936$$
$$x_{30} = 38.8062605608716$$
$$x_{1} = 39.7335557788732$$
$$x_{73} = 41.9478532144614$$
$$x_{39} = 46.0167410860528$$
$$x_{15} = 48.231038521641$$
$$x_{69} = 52.2999263932324$$
$$x_{48} = 54.5142238288206$$
$$x_{42} = 55.4415190468222$$
$$x_{66} = 60.7974091360002$$
$$x_{47} = 61.7247043540018$$
$$x_{34} = 63.93900178959$$
$$x_{31} = 68.0078896611814$$
$$x_{74} = 70.2221870967695$$
$$x_{35} = 74.2910749683609$$
$$x_{57} = 76.5053724039491$$
$$x_{9} = 77.4326676219507$$
$$x_{40} = 80.5742602755405$$
$$x_{20} = 82.7885577111287$$
$$x_{5} = 83.7158529291303$$
$$x_{7} = 85.9301503647185$$
$$x_{12} = 89.9990382363099$$
$$x_{72} = 92.2133356718981$$
$$x_{61} = 96.2822235434895$$
$$x_{58} = 98.4965209790777$$
$$x_{68} = 99.4238161970793$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{52}$$
For example, let's take the point
$$x_{0} = x_{52} - \frac{1}{10}$$
=
$$-143.406113347336 + - \frac{1}{10}$$
=
$$-143.506113347336$$
substitute to the expression
$$\left|{\tan{\left(t \right)}}\right| > 2$$
$$\left|{\tan{\left(t \right)}}\right| > 2$$
one of the solutions of our inequality is:
$$x < -143.406113347336$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < -143.406113347336$$
$$x > -99.4238161970793 \wedge x < -98.4965209790777$$
$$x > -96.2822235434895 \wedge x < -93.1406308898997$$
$$x > -92.2133356718981 \wedge x < -89.9990382363099$$
$$x > -85.9301503647185 \wedge x < -83.7158529291303$$
$$x > -79.6469650575389 \wedge x < -77.4326676219507$$
$$x > -76.5053724039491 \wedge x < -74.2910749683609$$
$$x > -71.1494823147711 \wedge x < -70.2221870967695$$
$$x > -68.0078896611814 \wedge x < -63.93900178959$$
$$x > -61.7247043540018 \wedge x < -57.6558164824104$$
$$x > -55.4415190468222 \wedge x < -54.5142238288206$$
$$x > -52.2999263932324 \wedge x < -49.1583337396426$$
$$x > -48.231038521641 \wedge x < -46.0167410860528$$
$$x > -41.9478532144614 \wedge x < -39.7335557788732$$
$$x > -35.6646679072818 \wedge x < -33.4503704716936$$
$$x > -32.523075253692 \wedge x < -30.3087778181038$$
$$x > -27.167185164514 \wedge x < -26.2398899465124$$
$$x > -24.0255925109243 \wedge x < -19.9567046393328$$
$$x > -17.7424072037447 \wedge x < -13.6735193321533$$
$$x > -11.4592218965651 \wedge x < -10.5319266785635$$
$$x > -8.31762924297529 \wedge x < -5.1760365893855$$
$$x > -4.24874137138388 \wedge x < -2.0344439357957$$
$$x > 2.0344439357957 \wedge x < 4.24874137138388$$
$$x > 8.31762924297529 \wedge x < 10.5319266785635$$
$$x > 11.4592218965651 \wedge x < 13.6735193321533$$
$$x > 16.8151119857431 \wedge x < 17.7424072037447$$
$$x > 19.9567046393328 \wedge x < 24.0255925109243$$
$$x > 26.2398899465124 \wedge x < 30.3087778181038$$
$$x > 32.523075253692 \wedge x < 33.4503704716936$$
$$x > 38.8062605608716 \wedge x < 39.7335557788732$$
$$x > 41.9478532144614 \wedge x < 46.0167410860528$$
$$x > 48.231038521641 \wedge x < 52.2999263932324$$
$$x > 54.5142238288206 \wedge x < 55.4415190468222$$
$$x > 60.7974091360002 \wedge x < 61.7247043540018$$
$$x > 63.93900178959 \wedge x < 68.0078896611814$$
$$x > 70.2221870967695 \wedge x < 74.2910749683609$$
$$x > 76.5053724039491 \wedge x < 77.4326676219507$$
$$x > 80.5742602755405 \wedge x < 82.7885577111287$$
$$x > 83.7158529291303 \wedge x < 85.9301503647185$$
$$x > 89.9990382363099 \wedge x < 92.2133356718981$$
$$x > 96.2822235434895 \wedge x < 98.4965209790777$$
$$x > 99.4238161970793$$
$$\left|{\tan{\left(t \right)}}\right| > 2$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{\tan{\left(t \right)}}\right| = 2$$
Solve:
Given the equation
$$\left|{\tan{\left(t \right)}}\right| = 2$$
transform
$$\left|{\tan{\left(t \right)}}\right| - 2 = 0$$
$$\left|{\tan{\left(t \right)}}\right| - 2 = 0$$
Do replacement
$$w = \left|{\tan{\left(t \right)}}\right|$$
Move free summands (without w)
from left part to right part, we given:
$$w = 2$$
We get the answer: w = 2
do backward replacement
$$\left|{\tan{\left(t \right)}}\right| = w$$
substitute w:
$$x_{1} = 39.7335557788732$$
$$x_{2} = 30.3087778181038$$
$$x_{3} = -11.4592218965651$$
$$x_{4} = -54.5142238288206$$
$$x_{5} = 83.7158529291303$$
$$x_{6} = -49.1583337396426$$
$$x_{7} = 85.9301503647185$$
$$x_{8} = 26.2398899465124$$
$$x_{9} = 77.4326676219507$$
$$x_{10} = 10.5319266785635$$
$$x_{11} = 8.31762924297529$$
$$x_{12} = 89.9990382363099$$
$$x_{13} = -41.9478532144614$$
$$x_{14} = -26.2398899465124$$
$$x_{15} = 48.231038521641$$
$$x_{16} = 17.7424072037447$$
$$x_{17} = -13.6735193321533$$
$$x_{18} = -33.4503704716936$$
$$x_{19} = -8.31762924297529$$
$$x_{20} = 82.7885577111287$$
$$x_{21} = -32.523075253692$$
$$x_{22} = -5.1760365893855$$
$$x_{23} = 2.0344439357957$$
$$x_{24} = -17.7424072037447$$
$$x_{25} = 11.4592218965651$$
$$x_{26} = 4.24874137138388$$
$$x_{27} = -89.9990382363099$$
$$x_{28} = -74.2910749683609$$
$$x_{29} = -4.24874137138388$$
$$x_{30} = 38.8062605608716$$
$$x_{31} = 68.0078896611814$$
$$x_{32} = -48.231038521641$$
$$x_{33} = 32.523075253692$$
$$x_{34} = 63.93900178959$$
$$x_{35} = 74.2910749683609$$
$$x_{36} = -71.1494823147711$$
$$x_{37} = -55.4415190468222$$
$$x_{38} = -70.2221870967695$$
$$x_{39} = 46.0167410860528$$
$$x_{40} = 80.5742602755405$$
$$x_{41} = 33.4503704716936$$
$$x_{42} = 55.4415190468222$$
$$x_{43} = -85.9301503647185$$
$$x_{44} = -27.167185164514$$
$$x_{45} = -83.7158529291303$$
$$x_{46} = -10.5319266785635$$
$$x_{47} = 61.7247043540018$$
$$x_{48} = 54.5142238288206$$
$$x_{49} = 13.6735193321533$$
$$x_{50} = -39.7335557788732$$
$$x_{51} = -96.2822235434895$$
$$x_{52} = -143.406113347336$$
$$x_{53} = -77.4326676219507$$
$$x_{54} = -35.6646679072818$$
$$x_{55} = -52.2999263932324$$
$$x_{56} = -98.4965209790777$$
$$x_{57} = 76.5053724039491$$
$$x_{58} = 98.4965209790777$$
$$x_{59} = 19.9567046393328$$
$$x_{60} = -68.0078896611814$$
$$x_{61} = 96.2822235434895$$
$$x_{62} = -63.93900178959$$
$$x_{63} = -30.3087778181038$$
$$x_{64} = 24.0255925109243$$
$$x_{65} = -24.0255925109243$$
$$x_{66} = 60.7974091360002$$
$$x_{67} = 16.8151119857431$$
$$x_{68} = 99.4238161970793$$
$$x_{69} = 52.2999263932324$$
$$x_{70} = -46.0167410860528$$
$$x_{71} = -99.4238161970793$$
$$x_{72} = 92.2133356718981$$
$$x_{73} = 41.9478532144614$$
$$x_{74} = 70.2221870967695$$
$$x_{75} = -61.7247043540018$$
$$x_{76} = -57.6558164824104$$
$$x_{77} = -92.2133356718981$$
$$x_{78} = -2.0344439357957$$
$$x_{79} = -93.1406308898997$$
$$x_{80} = -19.9567046393328$$
$$x_{81} = -76.5053724039491$$
$$x_{82} = -79.6469650575389$$
$$x_{1} = 39.7335557788732$$
$$x_{2} = 30.3087778181038$$
$$x_{3} = -11.4592218965651$$
$$x_{4} = -54.5142238288206$$
$$x_{5} = 83.7158529291303$$
$$x_{6} = -49.1583337396426$$
$$x_{7} = 85.9301503647185$$
$$x_{8} = 26.2398899465124$$
$$x_{9} = 77.4326676219507$$
$$x_{10} = 10.5319266785635$$
$$x_{11} = 8.31762924297529$$
$$x_{12} = 89.9990382363099$$
$$x_{13} = -41.9478532144614$$
$$x_{14} = -26.2398899465124$$
$$x_{15} = 48.231038521641$$
$$x_{16} = 17.7424072037447$$
$$x_{17} = -13.6735193321533$$
$$x_{18} = -33.4503704716936$$
$$x_{19} = -8.31762924297529$$
$$x_{20} = 82.7885577111287$$
$$x_{21} = -32.523075253692$$
$$x_{22} = -5.1760365893855$$
$$x_{23} = 2.0344439357957$$
$$x_{24} = -17.7424072037447$$
$$x_{25} = 11.4592218965651$$
$$x_{26} = 4.24874137138388$$
$$x_{27} = -89.9990382363099$$
$$x_{28} = -74.2910749683609$$
$$x_{29} = -4.24874137138388$$
$$x_{30} = 38.8062605608716$$
$$x_{31} = 68.0078896611814$$
$$x_{32} = -48.231038521641$$
$$x_{33} = 32.523075253692$$
$$x_{34} = 63.93900178959$$
$$x_{35} = 74.2910749683609$$
$$x_{36} = -71.1494823147711$$
$$x_{37} = -55.4415190468222$$
$$x_{38} = -70.2221870967695$$
$$x_{39} = 46.0167410860528$$
$$x_{40} = 80.5742602755405$$
$$x_{41} = 33.4503704716936$$
$$x_{42} = 55.4415190468222$$
$$x_{43} = -85.9301503647185$$
$$x_{44} = -27.167185164514$$
$$x_{45} = -83.7158529291303$$
$$x_{46} = -10.5319266785635$$
$$x_{47} = 61.7247043540018$$
$$x_{48} = 54.5142238288206$$
$$x_{49} = 13.6735193321533$$
$$x_{50} = -39.7335557788732$$
$$x_{51} = -96.2822235434895$$
$$x_{52} = -143.406113347336$$
$$x_{53} = -77.4326676219507$$
$$x_{54} = -35.6646679072818$$
$$x_{55} = -52.2999263932324$$
$$x_{56} = -98.4965209790777$$
$$x_{57} = 76.5053724039491$$
$$x_{58} = 98.4965209790777$$
$$x_{59} = 19.9567046393328$$
$$x_{60} = -68.0078896611814$$
$$x_{61} = 96.2822235434895$$
$$x_{62} = -63.93900178959$$
$$x_{63} = -30.3087778181038$$
$$x_{64} = 24.0255925109243$$
$$x_{65} = -24.0255925109243$$
$$x_{66} = 60.7974091360002$$
$$x_{67} = 16.8151119857431$$
$$x_{68} = 99.4238161970793$$
$$x_{69} = 52.2999263932324$$
$$x_{70} = -46.0167410860528$$
$$x_{71} = -99.4238161970793$$
$$x_{72} = 92.2133356718981$$
$$x_{73} = 41.9478532144614$$
$$x_{74} = 70.2221870967695$$
$$x_{75} = -61.7247043540018$$
$$x_{76} = -57.6558164824104$$
$$x_{77} = -92.2133356718981$$
$$x_{78} = -2.0344439357957$$
$$x_{79} = -93.1406308898997$$
$$x_{80} = -19.9567046393328$$
$$x_{81} = -76.5053724039491$$
$$x_{82} = -79.6469650575389$$
This roots
$$x_{52} = -143.406113347336$$
$$x_{71} = -99.4238161970793$$
$$x_{56} = -98.4965209790777$$
$$x_{51} = -96.2822235434895$$
$$x_{79} = -93.1406308898997$$
$$x_{77} = -92.2133356718981$$
$$x_{27} = -89.9990382363099$$
$$x_{43} = -85.9301503647185$$
$$x_{45} = -83.7158529291303$$
$$x_{82} = -79.6469650575389$$
$$x_{53} = -77.4326676219507$$
$$x_{81} = -76.5053724039491$$
$$x_{28} = -74.2910749683609$$
$$x_{36} = -71.1494823147711$$
$$x_{38} = -70.2221870967695$$
$$x_{60} = -68.0078896611814$$
$$x_{62} = -63.93900178959$$
$$x_{75} = -61.7247043540018$$
$$x_{76} = -57.6558164824104$$
$$x_{37} = -55.4415190468222$$
$$x_{4} = -54.5142238288206$$
$$x_{55} = -52.2999263932324$$
$$x_{6} = -49.1583337396426$$
$$x_{32} = -48.231038521641$$
$$x_{70} = -46.0167410860528$$
$$x_{13} = -41.9478532144614$$
$$x_{50} = -39.7335557788732$$
$$x_{54} = -35.6646679072818$$
$$x_{18} = -33.4503704716936$$
$$x_{21} = -32.523075253692$$
$$x_{63} = -30.3087778181038$$
$$x_{44} = -27.167185164514$$
$$x_{14} = -26.2398899465124$$
$$x_{65} = -24.0255925109243$$
$$x_{80} = -19.9567046393328$$
$$x_{24} = -17.7424072037447$$
$$x_{17} = -13.6735193321533$$
$$x_{3} = -11.4592218965651$$
$$x_{46} = -10.5319266785635$$
$$x_{19} = -8.31762924297529$$
$$x_{22} = -5.1760365893855$$
$$x_{29} = -4.24874137138388$$
$$x_{78} = -2.0344439357957$$
$$x_{23} = 2.0344439357957$$
$$x_{26} = 4.24874137138388$$
$$x_{11} = 8.31762924297529$$
$$x_{10} = 10.5319266785635$$
$$x_{25} = 11.4592218965651$$
$$x_{49} = 13.6735193321533$$
$$x_{67} = 16.8151119857431$$
$$x_{16} = 17.7424072037447$$
$$x_{59} = 19.9567046393328$$
$$x_{64} = 24.0255925109243$$
$$x_{8} = 26.2398899465124$$
$$x_{2} = 30.3087778181038$$
$$x_{33} = 32.523075253692$$
$$x_{41} = 33.4503704716936$$
$$x_{30} = 38.8062605608716$$
$$x_{1} = 39.7335557788732$$
$$x_{73} = 41.9478532144614$$
$$x_{39} = 46.0167410860528$$
$$x_{15} = 48.231038521641$$
$$x_{69} = 52.2999263932324$$
$$x_{48} = 54.5142238288206$$
$$x_{42} = 55.4415190468222$$
$$x_{66} = 60.7974091360002$$
$$x_{47} = 61.7247043540018$$
$$x_{34} = 63.93900178959$$
$$x_{31} = 68.0078896611814$$
$$x_{74} = 70.2221870967695$$
$$x_{35} = 74.2910749683609$$
$$x_{57} = 76.5053724039491$$
$$x_{9} = 77.4326676219507$$
$$x_{40} = 80.5742602755405$$
$$x_{20} = 82.7885577111287$$
$$x_{5} = 83.7158529291303$$
$$x_{7} = 85.9301503647185$$
$$x_{12} = 89.9990382363099$$
$$x_{72} = 92.2133356718981$$
$$x_{61} = 96.2822235434895$$
$$x_{58} = 98.4965209790777$$
$$x_{68} = 99.4238161970793$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{52}$$
For example, let's take the point
$$x_{0} = x_{52} - \frac{1}{10}$$
=
$$-143.406113347336 + - \frac{1}{10}$$
=
$$-143.506113347336$$
substitute to the expression
$$\left|{\tan{\left(t \right)}}\right| > 2$$
$$\left|{\tan{\left(t \right)}}\right| > 2$$
|tan(t)| > 2
one of the solutions of our inequality is:
$$x < -143.406113347336$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
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x52 x71 x56 x51 x79 x77 x27 x43 x45 x82 x53 x81 x28 x36 x38 x60 x62 x75 x76 x37 x4 x55 x6 x32 x70 x13 x50 x54 x18 x21 x63 x44 x14 x65 x80 x24 x17 x3 x46 x19 x22 x29 x78 x23 x26 x11 x10 x25 x49 x67 x16 x59 x64 x8 x2 x33 x41 x30 x1 x73 x39 x15 x69 x48 x42 x66 x47 x34 x31 x74 x35 x57 x9 x40 x20 x5 x7 x12 x72 x61 x58 x68Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < -143.406113347336$$
$$x > -99.4238161970793 \wedge x < -98.4965209790777$$
$$x > -96.2822235434895 \wedge x < -93.1406308898997$$
$$x > -92.2133356718981 \wedge x < -89.9990382363099$$
$$x > -85.9301503647185 \wedge x < -83.7158529291303$$
$$x > -79.6469650575389 \wedge x < -77.4326676219507$$
$$x > -76.5053724039491 \wedge x < -74.2910749683609$$
$$x > -71.1494823147711 \wedge x < -70.2221870967695$$
$$x > -68.0078896611814 \wedge x < -63.93900178959$$
$$x > -61.7247043540018 \wedge x < -57.6558164824104$$
$$x > -55.4415190468222 \wedge x < -54.5142238288206$$
$$x > -52.2999263932324 \wedge x < -49.1583337396426$$
$$x > -48.231038521641 \wedge x < -46.0167410860528$$
$$x > -41.9478532144614 \wedge x < -39.7335557788732$$
$$x > -35.6646679072818 \wedge x < -33.4503704716936$$
$$x > -32.523075253692 \wedge x < -30.3087778181038$$
$$x > -27.167185164514 \wedge x < -26.2398899465124$$
$$x > -24.0255925109243 \wedge x < -19.9567046393328$$
$$x > -17.7424072037447 \wedge x < -13.6735193321533$$
$$x > -11.4592218965651 \wedge x < -10.5319266785635$$
$$x > -8.31762924297529 \wedge x < -5.1760365893855$$
$$x > -4.24874137138388 \wedge x < -2.0344439357957$$
$$x > 2.0344439357957 \wedge x < 4.24874137138388$$
$$x > 8.31762924297529 \wedge x < 10.5319266785635$$
$$x > 11.4592218965651 \wedge x < 13.6735193321533$$
$$x > 16.8151119857431 \wedge x < 17.7424072037447$$
$$x > 19.9567046393328 \wedge x < 24.0255925109243$$
$$x > 26.2398899465124 \wedge x < 30.3087778181038$$
$$x > 32.523075253692 \wedge x < 33.4503704716936$$
$$x > 38.8062605608716 \wedge x < 39.7335557788732$$
$$x > 41.9478532144614 \wedge x < 46.0167410860528$$
$$x > 48.231038521641 \wedge x < 52.2999263932324$$
$$x > 54.5142238288206 \wedge x < 55.4415190468222$$
$$x > 60.7974091360002 \wedge x < 61.7247043540018$$
$$x > 63.93900178959 \wedge x < 68.0078896611814$$
$$x > 70.2221870967695 \wedge x < 74.2910749683609$$
$$x > 76.5053724039491 \wedge x < 77.4326676219507$$
$$x > 80.5742602755405 \wedge x < 82.7885577111287$$
$$x > 83.7158529291303 \wedge x < 85.9301503647185$$
$$x > 89.9990382363099 \wedge x < 92.2133356718981$$
$$x > 96.2822235434895 \wedge x < 98.4965209790777$$
$$x > 99.4238161970793$$