Mister Exam
|tan(x)|>=sqrt3 inequation
The solution
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___ |tan(x)| >= \/ 3
$$\left|{\tan{\left(x \right)}}\right| \geq \sqrt{3}$$
Abs(tan(x)) >= sqrt(3)
Detail solution
Given the inequality:
$$\left|{\tan{\left(x \right)}}\right| \geq \sqrt{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{\tan{\left(x \right)}}\right| = \sqrt{3}$$
Solve:
Given the equation
$$\left|{\tan{\left(x \right)}}\right| = \sqrt{3}$$
transform
$$\left|{\tan{\left(x \right)}}\right| - \sqrt{3} - 1 = 0$$
$$\left|{\tan{\left(x \right)}}\right| - \sqrt{3} - 1 = 0$$
Do replacement
$$w = \left|{\tan{\left(x \right)}}\right|$$
Expand brackets in the left part
Move free summands (without w)
from left part to right part, we given:
$$w - \sqrt{3} = 1$$
Divide both parts of the equation by (w - sqrt(3))/w
We get the answer: w = 1 + sqrt(3)
do backward replacement
$$\left|{\tan{\left(x \right)}}\right| = w$$
substitute w:
$$x_{1} = 96.342174710087$$
$$x_{2} = -86.9173967493176$$
$$x_{3} = 82.7286065445312$$
$$x_{4} = -57.5958653158129$$
$$x_{5} = -2.0943951023932$$
$$x_{6} = -99.4837673636768$$
$$x_{7} = -96.342174710087$$
$$x_{8} = 41.8879020478639$$
$$x_{9} = -92.1533845053006$$
$$x_{10} = 39.7935069454707$$
$$x_{11} = -13.6135681655558$$
$$x_{12} = 70.162235930172$$
$$x_{13} = 54.4542726622231$$
$$x_{14} = 80.634211442138$$
$$x_{15} = -39.7935069454707$$
$$x_{16} = 48.1710873550435$$
$$x_{17} = -41.8879020478639$$
$$x_{18} = 67.0206432765823$$
$$x_{19} = 63.8790506229925$$
$$x_{20} = 8.37758040957278$$
$$x_{21} = 23.0383461263252$$
$$x_{22} = -74.3510261349584$$
$$x_{23} = -82.7286065445312$$
$$x_{24} = 89.0117918517108$$
$$x_{25} = -54.4542726622231$$
$$x_{26} = -19.8967534727354$$
$$x_{27} = -8.37758040957278$$
$$x_{28} = 71.2094334813686$$
$$x_{29} = 98.4365698124802$$
$$x_{30} = 16.7551608191456$$
$$x_{31} = -77.4926187885482$$
$$x_{32} = 32.4631240870945$$
$$x_{33} = 1.0471975511966$$
$$x_{34} = -71.2094334813686$$
$$x_{35} = -55.5014702134197$$
$$x_{36} = 17.8023583703422$$
$$x_{37} = 55.5014702134197$$
$$x_{38} = 30.3687289847013$$
$$x_{39} = 60.7374579694027$$
$$x_{40} = -27.2271363311115$$
$$x_{41} = -90.0589894029074$$
$$x_{42} = 38.7463093942741$$
$$x_{43} = 19.8967534727354$$
$$x_{44} = 85.870199198121$$
$$x_{45} = 26.1799387799149$$
$$x_{46} = 77.4926187885482$$
$$x_{47} = -93.2005820564972$$
$$x_{48} = 24.0855436775217$$
$$x_{49} = 61.7846555205993$$
$$x_{50} = -98.4365698124802$$
$$x_{51} = 45.0294947014537$$
$$x_{52} = -63.8790506229925$$
$$x_{53} = -16.7551608191456$$
$$x_{54} = -30.3687289847013$$
$$x_{55} = 92.1533845053006$$
$$x_{56} = -17.8023583703422$$
$$x_{57} = -20.943951023932$$
$$x_{58} = 2.0943951023932$$
$$x_{59} = -60.7374579694027$$
$$x_{60} = -85.870199198121$$
$$x_{61} = 46.0766922526503$$
$$x_{62} = 13.6135681655558$$
$$x_{63} = 99.4837673636768$$
$$x_{64} = -32.4631240870945$$
$$x_{65} = -68.0678408277789$$
$$x_{66} = 27.2271363311115$$
$$x_{67} = -5.23598775598299$$
$$x_{68} = 10.471975511966$$
$$x_{69} = -46.0766922526503$$
$$x_{70} = 49.2182849062401$$
$$x_{71} = -49.2182849062401$$
$$x_{72} = -52.3598775598299$$
$$x_{73} = -79.5870138909414$$
$$x_{74} = -10.471975511966$$
$$x_{75} = 74.3510261349584$$
$$x_{76} = -24.0855436775217$$
$$x_{77} = -61.7846555205993$$
$$x_{78} = 4.18879020478639$$
$$x_{79} = -70.162235930172$$
$$x_{80} = -4.18879020478639$$
$$x_{81} = 5.23598775598299$$
$$x_{82} = 68.0678408277789$$
$$x_{83} = -76.4454212373516$$
$$x_{84} = 90.0589894029074$$
$$x_{85} = -11.5191730631626$$
$$x_{86} = -33.5103216382911$$
$$x_{87} = 93.2005820564972$$
$$x_{88} = 11.5191730631626$$
$$x_{89} = -83.7758040957278$$
$$x_{90} = -35.6047167406843$$
$$x_{91} = -26.1799387799149$$
$$x_{92} = 83.7758040957278$$
$$x_{93} = -48.1710873550435$$
$$x_{94} = 76.4454212373516$$
$$x_{95} = 52.3598775598299$$
$$x_{96} = 33.5103216382911$$
$$x_{97} = -38.7463093942741$$
$$x_{1} = 96.342174710087$$
$$x_{2} = -86.9173967493176$$
$$x_{3} = 82.7286065445312$$
$$x_{4} = -57.5958653158129$$
$$x_{5} = -2.0943951023932$$
$$x_{6} = -99.4837673636768$$
$$x_{7} = -96.342174710087$$
$$x_{8} = 41.8879020478639$$
$$x_{9} = -92.1533845053006$$
$$x_{10} = 39.7935069454707$$
$$x_{11} = -13.6135681655558$$
$$x_{12} = 70.162235930172$$
$$x_{13} = 54.4542726622231$$
$$x_{14} = 80.634211442138$$
$$x_{15} = -39.7935069454707$$
$$x_{16} = 48.1710873550435$$
$$x_{17} = -41.8879020478639$$
$$x_{18} = 67.0206432765823$$
$$x_{19} = 63.8790506229925$$
$$x_{20} = 8.37758040957278$$
$$x_{21} = 23.0383461263252$$
$$x_{22} = -74.3510261349584$$
$$x_{23} = -82.7286065445312$$
$$x_{24} = 89.0117918517108$$
$$x_{25} = -54.4542726622231$$
$$x_{26} = -19.8967534727354$$
$$x_{27} = -8.37758040957278$$
$$x_{28} = 71.2094334813686$$
$$x_{29} = 98.4365698124802$$
$$x_{30} = 16.7551608191456$$
$$x_{31} = -77.4926187885482$$
$$x_{32} = 32.4631240870945$$
$$x_{33} = 1.0471975511966$$
$$x_{34} = -71.2094334813686$$
$$x_{35} = -55.5014702134197$$
$$x_{36} = 17.8023583703422$$
$$x_{37} = 55.5014702134197$$
$$x_{38} = 30.3687289847013$$
$$x_{39} = 60.7374579694027$$
$$x_{40} = -27.2271363311115$$
$$x_{41} = -90.0589894029074$$
$$x_{42} = 38.7463093942741$$
$$x_{43} = 19.8967534727354$$
$$x_{44} = 85.870199198121$$
$$x_{45} = 26.1799387799149$$
$$x_{46} = 77.4926187885482$$
$$x_{47} = -93.2005820564972$$
$$x_{48} = 24.0855436775217$$
$$x_{49} = 61.7846555205993$$
$$x_{50} = -98.4365698124802$$
$$x_{51} = 45.0294947014537$$
$$x_{52} = -63.8790506229925$$
$$x_{53} = -16.7551608191456$$
$$x_{54} = -30.3687289847013$$
$$x_{55} = 92.1533845053006$$
$$x_{56} = -17.8023583703422$$
$$x_{57} = -20.943951023932$$
$$x_{58} = 2.0943951023932$$
$$x_{59} = -60.7374579694027$$
$$x_{60} = -85.870199198121$$
$$x_{61} = 46.0766922526503$$
$$x_{62} = 13.6135681655558$$
$$x_{63} = 99.4837673636768$$
$$x_{64} = -32.4631240870945$$
$$x_{65} = -68.0678408277789$$
$$x_{66} = 27.2271363311115$$
$$x_{67} = -5.23598775598299$$
$$x_{68} = 10.471975511966$$
$$x_{69} = -46.0766922526503$$
$$x_{70} = 49.2182849062401$$
$$x_{71} = -49.2182849062401$$
$$x_{72} = -52.3598775598299$$
$$x_{73} = -79.5870138909414$$
$$x_{74} = -10.471975511966$$
$$x_{75} = 74.3510261349584$$
$$x_{76} = -24.0855436775217$$
$$x_{77} = -61.7846555205993$$
$$x_{78} = 4.18879020478639$$
$$x_{79} = -70.162235930172$$
$$x_{80} = -4.18879020478639$$
$$x_{81} = 5.23598775598299$$
$$x_{82} = 68.0678408277789$$
$$x_{83} = -76.4454212373516$$
$$x_{84} = 90.0589894029074$$
$$x_{85} = -11.5191730631626$$
$$x_{86} = -33.5103216382911$$
$$x_{87} = 93.2005820564972$$
$$x_{88} = 11.5191730631626$$
$$x_{89} = -83.7758040957278$$
$$x_{90} = -35.6047167406843$$
$$x_{91} = -26.1799387799149$$
$$x_{92} = 83.7758040957278$$
$$x_{93} = -48.1710873550435$$
$$x_{94} = 76.4454212373516$$
$$x_{95} = 52.3598775598299$$
$$x_{96} = 33.5103216382911$$
$$x_{97} = -38.7463093942741$$
This roots
$$x_{6} = -99.4837673636768$$
$$x_{50} = -98.4365698124802$$
$$x_{7} = -96.342174710087$$
$$x_{47} = -93.2005820564972$$
$$x_{9} = -92.1533845053006$$
$$x_{41} = -90.0589894029074$$
$$x_{2} = -86.9173967493176$$
$$x_{60} = -85.870199198121$$
$$x_{89} = -83.7758040957278$$
$$x_{23} = -82.7286065445312$$
$$x_{73} = -79.5870138909414$$
$$x_{31} = -77.4926187885482$$
$$x_{83} = -76.4454212373516$$
$$x_{22} = -74.3510261349584$$
$$x_{34} = -71.2094334813686$$
$$x_{79} = -70.162235930172$$
$$x_{65} = -68.0678408277789$$
$$x_{52} = -63.8790506229925$$
$$x_{77} = -61.7846555205993$$
$$x_{59} = -60.7374579694027$$
$$x_{4} = -57.5958653158129$$
$$x_{35} = -55.5014702134197$$
$$x_{25} = -54.4542726622231$$
$$x_{72} = -52.3598775598299$$
$$x_{71} = -49.2182849062401$$
$$x_{93} = -48.1710873550435$$
$$x_{69} = -46.0766922526503$$
$$x_{17} = -41.8879020478639$$
$$x_{15} = -39.7935069454707$$
$$x_{97} = -38.7463093942741$$
$$x_{90} = -35.6047167406843$$
$$x_{86} = -33.5103216382911$$
$$x_{64} = -32.4631240870945$$
$$x_{54} = -30.3687289847013$$
$$x_{40} = -27.2271363311115$$
$$x_{91} = -26.1799387799149$$
$$x_{76} = -24.0855436775217$$
$$x_{57} = -20.943951023932$$
$$x_{26} = -19.8967534727354$$
$$x_{56} = -17.8023583703422$$
$$x_{53} = -16.7551608191456$$
$$x_{11} = -13.6135681655558$$
$$x_{85} = -11.5191730631626$$
$$x_{74} = -10.471975511966$$
$$x_{27} = -8.37758040957278$$
$$x_{67} = -5.23598775598299$$
$$x_{80} = -4.18879020478639$$
$$x_{5} = -2.0943951023932$$
$$x_{33} = 1.0471975511966$$
$$x_{58} = 2.0943951023932$$
$$x_{78} = 4.18879020478639$$
$$x_{81} = 5.23598775598299$$
$$x_{20} = 8.37758040957278$$
$$x_{68} = 10.471975511966$$
$$x_{88} = 11.5191730631626$$
$$x_{62} = 13.6135681655558$$
$$x_{30} = 16.7551608191456$$
$$x_{36} = 17.8023583703422$$
$$x_{43} = 19.8967534727354$$
$$x_{21} = 23.0383461263252$$
$$x_{48} = 24.0855436775217$$
$$x_{45} = 26.1799387799149$$
$$x_{66} = 27.2271363311115$$
$$x_{38} = 30.3687289847013$$
$$x_{32} = 32.4631240870945$$
$$x_{96} = 33.5103216382911$$
$$x_{42} = 38.7463093942741$$
$$x_{10} = 39.7935069454707$$
$$x_{8} = 41.8879020478639$$
$$x_{51} = 45.0294947014537$$
$$x_{61} = 46.0766922526503$$
$$x_{16} = 48.1710873550435$$
$$x_{70} = 49.2182849062401$$
$$x_{95} = 52.3598775598299$$
$$x_{13} = 54.4542726622231$$
$$x_{37} = 55.5014702134197$$
$$x_{39} = 60.7374579694027$$
$$x_{49} = 61.7846555205993$$
$$x_{19} = 63.8790506229925$$
$$x_{18} = 67.0206432765823$$
$$x_{82} = 68.0678408277789$$
$$x_{12} = 70.162235930172$$
$$x_{28} = 71.2094334813686$$
$$x_{75} = 74.3510261349584$$
$$x_{94} = 76.4454212373516$$
$$x_{46} = 77.4926187885482$$
$$x_{14} = 80.634211442138$$
$$x_{3} = 82.7286065445312$$
$$x_{92} = 83.7758040957278$$
$$x_{44} = 85.870199198121$$
$$x_{24} = 89.0117918517108$$
$$x_{84} = 90.0589894029074$$
$$x_{55} = 92.1533845053006$$
$$x_{87} = 93.2005820564972$$
$$x_{1} = 96.342174710087$$
$$x_{29} = 98.4365698124802$$
$$x_{63} = 99.4837673636768$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{6}$$
For example, let's take the point
$$x_{0} = x_{6} - \frac{1}{10}$$
=
$$-99.4837673636768 + - \frac{1}{10}$$
=
$$-99.5837673636768$$
substitute to the expression
$$\left|{\tan{\left(x \right)}}\right| \geq \sqrt{3}$$
$$\left|{\tan{\left(-99.5837673636768 \right)}}\right| \geq \sqrt{3}$$
but
Then
$$x \leq -99.4837673636768$$
no execute
one of the solutions of our inequality is:
$$x \geq -99.4837673636768 \wedge x \leq -98.4365698124802$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -99.4837673636768 \wedge x \leq -98.4365698124802$$
$$x \geq -96.342174710087 \wedge x \leq -93.2005820564972$$
$$x \geq -92.1533845053006 \wedge x \leq -90.0589894029074$$
$$x \geq -86.9173967493176 \wedge x \leq -85.870199198121$$
$$x \geq -83.7758040957278 \wedge x \leq -82.7286065445312$$
$$x \geq -79.5870138909414 \wedge x \leq -77.4926187885482$$
$$x \geq -76.4454212373516 \wedge x \leq -74.3510261349584$$
$$x \geq -71.2094334813686 \wedge x \leq -70.162235930172$$
$$x \geq -68.0678408277789 \wedge x \leq -63.8790506229925$$
$$x \geq -61.7846555205993 \wedge x \leq -60.7374579694027$$
$$x \geq -57.5958653158129 \wedge x \leq -55.5014702134197$$
$$x \geq -54.4542726622231 \wedge x \leq -52.3598775598299$$
$$x \geq -49.2182849062401 \wedge x \leq -48.1710873550435$$
$$x \geq -46.0766922526503 \wedge x \leq -41.8879020478639$$
$$x \geq -39.7935069454707 \wedge x \leq -38.7463093942741$$
$$x \geq -35.6047167406843 \wedge x \leq -33.5103216382911$$
$$x \geq -32.4631240870945 \wedge x \leq -30.3687289847013$$
$$x \geq -27.2271363311115 \wedge x \leq -26.1799387799149$$
$$x \geq -24.0855436775217 \wedge x \leq -20.943951023932$$
$$x \geq -19.8967534727354 \wedge x \leq -17.8023583703422$$
$$x \geq -16.7551608191456 \wedge x \leq -13.6135681655558$$
$$x \geq -11.5191730631626 \wedge x \leq -10.471975511966$$
$$x \geq -8.37758040957278 \wedge x \leq -5.23598775598299$$
$$x \geq -4.18879020478639 \wedge x \leq -2.0943951023932$$
$$x \geq 1.0471975511966 \wedge x \leq 2.0943951023932$$
$$x \geq 4.18879020478639 \wedge x \leq 5.23598775598299$$
$$x \geq 8.37758040957278 \wedge x \leq 10.471975511966$$
$$x \geq 11.5191730631626 \wedge x \leq 13.6135681655558$$
$$x \geq 16.7551608191456 \wedge x \leq 17.8023583703422$$
$$x \geq 19.8967534727354 \wedge x \leq 23.0383461263252$$
$$x \geq 24.0855436775217 \wedge x \leq 26.1799387799149$$
$$x \geq 27.2271363311115 \wedge x \leq 30.3687289847013$$
$$x \geq 32.4631240870945 \wedge x \leq 33.5103216382911$$
$$x \geq 38.7463093942741 \wedge x \leq 39.7935069454707$$
$$x \geq 41.8879020478639 \wedge x \leq 45.0294947014537$$
$$x \geq 46.0766922526503 \wedge x \leq 48.1710873550435$$
$$x \geq 49.2182849062401 \wedge x \leq 52.3598775598299$$
$$x \geq 54.4542726622231 \wedge x \leq 55.5014702134197$$
$$x \geq 60.7374579694027 \wedge x \leq 61.7846555205993$$
$$x \geq 63.8790506229925 \wedge x \leq 67.0206432765823$$
$$x \geq 68.0678408277789 \wedge x \leq 70.162235930172$$
$$x \geq 71.2094334813686 \wedge x \leq 74.3510261349584$$
$$x \geq 76.4454212373516 \wedge x \leq 77.4926187885482$$
$$x \geq 80.634211442138 \wedge x \leq 82.7286065445312$$
$$x \geq 83.7758040957278 \wedge x \leq 85.870199198121$$
$$x \geq 89.0117918517108 \wedge x \leq 90.0589894029074$$
$$x \geq 92.1533845053006 \wedge x \leq 93.2005820564972$$
$$x \geq 96.342174710087 \wedge x \leq 98.4365698124802$$
$$x \geq 99.4837673636768$$
$$\left|{\tan{\left(x \right)}}\right| \geq \sqrt{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{\tan{\left(x \right)}}\right| = \sqrt{3}$$
Solve:
Given the equation
$$\left|{\tan{\left(x \right)}}\right| = \sqrt{3}$$
transform
$$\left|{\tan{\left(x \right)}}\right| - \sqrt{3} - 1 = 0$$
$$\left|{\tan{\left(x \right)}}\right| - \sqrt{3} - 1 = 0$$
Do replacement
$$w = \left|{\tan{\left(x \right)}}\right|$$
Expand brackets in the left part
-1 + w - sqrt3 = 0
Move free summands (without w)
from left part to right part, we given:
$$w - \sqrt{3} = 1$$
Divide both parts of the equation by (w - sqrt(3))/w
w = 1 / ((w - sqrt(3))/w)
We get the answer: w = 1 + sqrt(3)
do backward replacement
$$\left|{\tan{\left(x \right)}}\right| = w$$
substitute w:
$$x_{1} = 96.342174710087$$
$$x_{2} = -86.9173967493176$$
$$x_{3} = 82.7286065445312$$
$$x_{4} = -57.5958653158129$$
$$x_{5} = -2.0943951023932$$
$$x_{6} = -99.4837673636768$$
$$x_{7} = -96.342174710087$$
$$x_{8} = 41.8879020478639$$
$$x_{9} = -92.1533845053006$$
$$x_{10} = 39.7935069454707$$
$$x_{11} = -13.6135681655558$$
$$x_{12} = 70.162235930172$$
$$x_{13} = 54.4542726622231$$
$$x_{14} = 80.634211442138$$
$$x_{15} = -39.7935069454707$$
$$x_{16} = 48.1710873550435$$
$$x_{17} = -41.8879020478639$$
$$x_{18} = 67.0206432765823$$
$$x_{19} = 63.8790506229925$$
$$x_{20} = 8.37758040957278$$
$$x_{21} = 23.0383461263252$$
$$x_{22} = -74.3510261349584$$
$$x_{23} = -82.7286065445312$$
$$x_{24} = 89.0117918517108$$
$$x_{25} = -54.4542726622231$$
$$x_{26} = -19.8967534727354$$
$$x_{27} = -8.37758040957278$$
$$x_{28} = 71.2094334813686$$
$$x_{29} = 98.4365698124802$$
$$x_{30} = 16.7551608191456$$
$$x_{31} = -77.4926187885482$$
$$x_{32} = 32.4631240870945$$
$$x_{33} = 1.0471975511966$$
$$x_{34} = -71.2094334813686$$
$$x_{35} = -55.5014702134197$$
$$x_{36} = 17.8023583703422$$
$$x_{37} = 55.5014702134197$$
$$x_{38} = 30.3687289847013$$
$$x_{39} = 60.7374579694027$$
$$x_{40} = -27.2271363311115$$
$$x_{41} = -90.0589894029074$$
$$x_{42} = 38.7463093942741$$
$$x_{43} = 19.8967534727354$$
$$x_{44} = 85.870199198121$$
$$x_{45} = 26.1799387799149$$
$$x_{46} = 77.4926187885482$$
$$x_{47} = -93.2005820564972$$
$$x_{48} = 24.0855436775217$$
$$x_{49} = 61.7846555205993$$
$$x_{50} = -98.4365698124802$$
$$x_{51} = 45.0294947014537$$
$$x_{52} = -63.8790506229925$$
$$x_{53} = -16.7551608191456$$
$$x_{54} = -30.3687289847013$$
$$x_{55} = 92.1533845053006$$
$$x_{56} = -17.8023583703422$$
$$x_{57} = -20.943951023932$$
$$x_{58} = 2.0943951023932$$
$$x_{59} = -60.7374579694027$$
$$x_{60} = -85.870199198121$$
$$x_{61} = 46.0766922526503$$
$$x_{62} = 13.6135681655558$$
$$x_{63} = 99.4837673636768$$
$$x_{64} = -32.4631240870945$$
$$x_{65} = -68.0678408277789$$
$$x_{66} = 27.2271363311115$$
$$x_{67} = -5.23598775598299$$
$$x_{68} = 10.471975511966$$
$$x_{69} = -46.0766922526503$$
$$x_{70} = 49.2182849062401$$
$$x_{71} = -49.2182849062401$$
$$x_{72} = -52.3598775598299$$
$$x_{73} = -79.5870138909414$$
$$x_{74} = -10.471975511966$$
$$x_{75} = 74.3510261349584$$
$$x_{76} = -24.0855436775217$$
$$x_{77} = -61.7846555205993$$
$$x_{78} = 4.18879020478639$$
$$x_{79} = -70.162235930172$$
$$x_{80} = -4.18879020478639$$
$$x_{81} = 5.23598775598299$$
$$x_{82} = 68.0678408277789$$
$$x_{83} = -76.4454212373516$$
$$x_{84} = 90.0589894029074$$
$$x_{85} = -11.5191730631626$$
$$x_{86} = -33.5103216382911$$
$$x_{87} = 93.2005820564972$$
$$x_{88} = 11.5191730631626$$
$$x_{89} = -83.7758040957278$$
$$x_{90} = -35.6047167406843$$
$$x_{91} = -26.1799387799149$$
$$x_{92} = 83.7758040957278$$
$$x_{93} = -48.1710873550435$$
$$x_{94} = 76.4454212373516$$
$$x_{95} = 52.3598775598299$$
$$x_{96} = 33.5103216382911$$
$$x_{97} = -38.7463093942741$$
$$x_{1} = 96.342174710087$$
$$x_{2} = -86.9173967493176$$
$$x_{3} = 82.7286065445312$$
$$x_{4} = -57.5958653158129$$
$$x_{5} = -2.0943951023932$$
$$x_{6} = -99.4837673636768$$
$$x_{7} = -96.342174710087$$
$$x_{8} = 41.8879020478639$$
$$x_{9} = -92.1533845053006$$
$$x_{10} = 39.7935069454707$$
$$x_{11} = -13.6135681655558$$
$$x_{12} = 70.162235930172$$
$$x_{13} = 54.4542726622231$$
$$x_{14} = 80.634211442138$$
$$x_{15} = -39.7935069454707$$
$$x_{16} = 48.1710873550435$$
$$x_{17} = -41.8879020478639$$
$$x_{18} = 67.0206432765823$$
$$x_{19} = 63.8790506229925$$
$$x_{20} = 8.37758040957278$$
$$x_{21} = 23.0383461263252$$
$$x_{22} = -74.3510261349584$$
$$x_{23} = -82.7286065445312$$
$$x_{24} = 89.0117918517108$$
$$x_{25} = -54.4542726622231$$
$$x_{26} = -19.8967534727354$$
$$x_{27} = -8.37758040957278$$
$$x_{28} = 71.2094334813686$$
$$x_{29} = 98.4365698124802$$
$$x_{30} = 16.7551608191456$$
$$x_{31} = -77.4926187885482$$
$$x_{32} = 32.4631240870945$$
$$x_{33} = 1.0471975511966$$
$$x_{34} = -71.2094334813686$$
$$x_{35} = -55.5014702134197$$
$$x_{36} = 17.8023583703422$$
$$x_{37} = 55.5014702134197$$
$$x_{38} = 30.3687289847013$$
$$x_{39} = 60.7374579694027$$
$$x_{40} = -27.2271363311115$$
$$x_{41} = -90.0589894029074$$
$$x_{42} = 38.7463093942741$$
$$x_{43} = 19.8967534727354$$
$$x_{44} = 85.870199198121$$
$$x_{45} = 26.1799387799149$$
$$x_{46} = 77.4926187885482$$
$$x_{47} = -93.2005820564972$$
$$x_{48} = 24.0855436775217$$
$$x_{49} = 61.7846555205993$$
$$x_{50} = -98.4365698124802$$
$$x_{51} = 45.0294947014537$$
$$x_{52} = -63.8790506229925$$
$$x_{53} = -16.7551608191456$$
$$x_{54} = -30.3687289847013$$
$$x_{55} = 92.1533845053006$$
$$x_{56} = -17.8023583703422$$
$$x_{57} = -20.943951023932$$
$$x_{58} = 2.0943951023932$$
$$x_{59} = -60.7374579694027$$
$$x_{60} = -85.870199198121$$
$$x_{61} = 46.0766922526503$$
$$x_{62} = 13.6135681655558$$
$$x_{63} = 99.4837673636768$$
$$x_{64} = -32.4631240870945$$
$$x_{65} = -68.0678408277789$$
$$x_{66} = 27.2271363311115$$
$$x_{67} = -5.23598775598299$$
$$x_{68} = 10.471975511966$$
$$x_{69} = -46.0766922526503$$
$$x_{70} = 49.2182849062401$$
$$x_{71} = -49.2182849062401$$
$$x_{72} = -52.3598775598299$$
$$x_{73} = -79.5870138909414$$
$$x_{74} = -10.471975511966$$
$$x_{75} = 74.3510261349584$$
$$x_{76} = -24.0855436775217$$
$$x_{77} = -61.7846555205993$$
$$x_{78} = 4.18879020478639$$
$$x_{79} = -70.162235930172$$
$$x_{80} = -4.18879020478639$$
$$x_{81} = 5.23598775598299$$
$$x_{82} = 68.0678408277789$$
$$x_{83} = -76.4454212373516$$
$$x_{84} = 90.0589894029074$$
$$x_{85} = -11.5191730631626$$
$$x_{86} = -33.5103216382911$$
$$x_{87} = 93.2005820564972$$
$$x_{88} = 11.5191730631626$$
$$x_{89} = -83.7758040957278$$
$$x_{90} = -35.6047167406843$$
$$x_{91} = -26.1799387799149$$
$$x_{92} = 83.7758040957278$$
$$x_{93} = -48.1710873550435$$
$$x_{94} = 76.4454212373516$$
$$x_{95} = 52.3598775598299$$
$$x_{96} = 33.5103216382911$$
$$x_{97} = -38.7463093942741$$
This roots
$$x_{6} = -99.4837673636768$$
$$x_{50} = -98.4365698124802$$
$$x_{7} = -96.342174710087$$
$$x_{47} = -93.2005820564972$$
$$x_{9} = -92.1533845053006$$
$$x_{41} = -90.0589894029074$$
$$x_{2} = -86.9173967493176$$
$$x_{60} = -85.870199198121$$
$$x_{89} = -83.7758040957278$$
$$x_{23} = -82.7286065445312$$
$$x_{73} = -79.5870138909414$$
$$x_{31} = -77.4926187885482$$
$$x_{83} = -76.4454212373516$$
$$x_{22} = -74.3510261349584$$
$$x_{34} = -71.2094334813686$$
$$x_{79} = -70.162235930172$$
$$x_{65} = -68.0678408277789$$
$$x_{52} = -63.8790506229925$$
$$x_{77} = -61.7846555205993$$
$$x_{59} = -60.7374579694027$$
$$x_{4} = -57.5958653158129$$
$$x_{35} = -55.5014702134197$$
$$x_{25} = -54.4542726622231$$
$$x_{72} = -52.3598775598299$$
$$x_{71} = -49.2182849062401$$
$$x_{93} = -48.1710873550435$$
$$x_{69} = -46.0766922526503$$
$$x_{17} = -41.8879020478639$$
$$x_{15} = -39.7935069454707$$
$$x_{97} = -38.7463093942741$$
$$x_{90} = -35.6047167406843$$
$$x_{86} = -33.5103216382911$$
$$x_{64} = -32.4631240870945$$
$$x_{54} = -30.3687289847013$$
$$x_{40} = -27.2271363311115$$
$$x_{91} = -26.1799387799149$$
$$x_{76} = -24.0855436775217$$
$$x_{57} = -20.943951023932$$
$$x_{26} = -19.8967534727354$$
$$x_{56} = -17.8023583703422$$
$$x_{53} = -16.7551608191456$$
$$x_{11} = -13.6135681655558$$
$$x_{85} = -11.5191730631626$$
$$x_{74} = -10.471975511966$$
$$x_{27} = -8.37758040957278$$
$$x_{67} = -5.23598775598299$$
$$x_{80} = -4.18879020478639$$
$$x_{5} = -2.0943951023932$$
$$x_{33} = 1.0471975511966$$
$$x_{58} = 2.0943951023932$$
$$x_{78} = 4.18879020478639$$
$$x_{81} = 5.23598775598299$$
$$x_{20} = 8.37758040957278$$
$$x_{68} = 10.471975511966$$
$$x_{88} = 11.5191730631626$$
$$x_{62} = 13.6135681655558$$
$$x_{30} = 16.7551608191456$$
$$x_{36} = 17.8023583703422$$
$$x_{43} = 19.8967534727354$$
$$x_{21} = 23.0383461263252$$
$$x_{48} = 24.0855436775217$$
$$x_{45} = 26.1799387799149$$
$$x_{66} = 27.2271363311115$$
$$x_{38} = 30.3687289847013$$
$$x_{32} = 32.4631240870945$$
$$x_{96} = 33.5103216382911$$
$$x_{42} = 38.7463093942741$$
$$x_{10} = 39.7935069454707$$
$$x_{8} = 41.8879020478639$$
$$x_{51} = 45.0294947014537$$
$$x_{61} = 46.0766922526503$$
$$x_{16} = 48.1710873550435$$
$$x_{70} = 49.2182849062401$$
$$x_{95} = 52.3598775598299$$
$$x_{13} = 54.4542726622231$$
$$x_{37} = 55.5014702134197$$
$$x_{39} = 60.7374579694027$$
$$x_{49} = 61.7846555205993$$
$$x_{19} = 63.8790506229925$$
$$x_{18} = 67.0206432765823$$
$$x_{82} = 68.0678408277789$$
$$x_{12} = 70.162235930172$$
$$x_{28} = 71.2094334813686$$
$$x_{75} = 74.3510261349584$$
$$x_{94} = 76.4454212373516$$
$$x_{46} = 77.4926187885482$$
$$x_{14} = 80.634211442138$$
$$x_{3} = 82.7286065445312$$
$$x_{92} = 83.7758040957278$$
$$x_{44} = 85.870199198121$$
$$x_{24} = 89.0117918517108$$
$$x_{84} = 90.0589894029074$$
$$x_{55} = 92.1533845053006$$
$$x_{87} = 93.2005820564972$$
$$x_{1} = 96.342174710087$$
$$x_{29} = 98.4365698124802$$
$$x_{63} = 99.4837673636768$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{6}$$
For example, let's take the point
$$x_{0} = x_{6} - \frac{1}{10}$$
=
$$-99.4837673636768 + - \frac{1}{10}$$
=
$$-99.5837673636768$$
substitute to the expression
$$\left|{\tan{\left(x \right)}}\right| \geq \sqrt{3}$$
$$\left|{\tan{\left(-99.5837673636768 \right)}}\right| \geq \sqrt{3}$$
___
1.39013233537385 >= \/ 3
but
___
1.39013233537385 < \/ 3
Then
$$x \leq -99.4837673636768$$
no execute
one of the solutions of our inequality is:
$$x \geq -99.4837673636768 \wedge x \leq -98.4365698124802$$
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x6 x50 x7 x47 x9 x41 x2 x60 x89 x23 x73 x31 x83 x22 x34 x79 x65 x52 x77 x59 x4 x35 x25 x72 x71 x93 x69 x17 x15 x97 x90 x86 x64 x54 x40 x91 x76 x57 x26 x56 x53 x11 x85 x74 x27 x67 x80 x5 x33 x58 x78 x81 x20 x68 x88 x62 x30 x36 x43 x21 x48 x45 x66 x38 x32 x96 x42 x10 x8 x51 x61 x16 x70 x95 x13 x37 x39 x49 x19 x18 x82 x12 x28 x75 x94 x46 x14 x3 x92 x44 x24 x84 x55 x87 x1 x29 x63Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -99.4837673636768 \wedge x \leq -98.4365698124802$$
$$x \geq -96.342174710087 \wedge x \leq -93.2005820564972$$
$$x \geq -92.1533845053006 \wedge x \leq -90.0589894029074$$
$$x \geq -86.9173967493176 \wedge x \leq -85.870199198121$$
$$x \geq -83.7758040957278 \wedge x \leq -82.7286065445312$$
$$x \geq -79.5870138909414 \wedge x \leq -77.4926187885482$$
$$x \geq -76.4454212373516 \wedge x \leq -74.3510261349584$$
$$x \geq -71.2094334813686 \wedge x \leq -70.162235930172$$
$$x \geq -68.0678408277789 \wedge x \leq -63.8790506229925$$
$$x \geq -61.7846555205993 \wedge x \leq -60.7374579694027$$
$$x \geq -57.5958653158129 \wedge x \leq -55.5014702134197$$
$$x \geq -54.4542726622231 \wedge x \leq -52.3598775598299$$
$$x \geq -49.2182849062401 \wedge x \leq -48.1710873550435$$
$$x \geq -46.0766922526503 \wedge x \leq -41.8879020478639$$
$$x \geq -39.7935069454707 \wedge x \leq -38.7463093942741$$
$$x \geq -35.6047167406843 \wedge x \leq -33.5103216382911$$
$$x \geq -32.4631240870945 \wedge x \leq -30.3687289847013$$
$$x \geq -27.2271363311115 \wedge x \leq -26.1799387799149$$
$$x \geq -24.0855436775217 \wedge x \leq -20.943951023932$$
$$x \geq -19.8967534727354 \wedge x \leq -17.8023583703422$$
$$x \geq -16.7551608191456 \wedge x \leq -13.6135681655558$$
$$x \geq -11.5191730631626 \wedge x \leq -10.471975511966$$
$$x \geq -8.37758040957278 \wedge x \leq -5.23598775598299$$
$$x \geq -4.18879020478639 \wedge x \leq -2.0943951023932$$
$$x \geq 1.0471975511966 \wedge x \leq 2.0943951023932$$
$$x \geq 4.18879020478639 \wedge x \leq 5.23598775598299$$
$$x \geq 8.37758040957278 \wedge x \leq 10.471975511966$$
$$x \geq 11.5191730631626 \wedge x \leq 13.6135681655558$$
$$x \geq 16.7551608191456 \wedge x \leq 17.8023583703422$$
$$x \geq 19.8967534727354 \wedge x \leq 23.0383461263252$$
$$x \geq 24.0855436775217 \wedge x \leq 26.1799387799149$$
$$x \geq 27.2271363311115 \wedge x \leq 30.3687289847013$$
$$x \geq 32.4631240870945 \wedge x \leq 33.5103216382911$$
$$x \geq 38.7463093942741 \wedge x \leq 39.7935069454707$$
$$x \geq 41.8879020478639 \wedge x \leq 45.0294947014537$$
$$x \geq 46.0766922526503 \wedge x \leq 48.1710873550435$$
$$x \geq 49.2182849062401 \wedge x \leq 52.3598775598299$$
$$x \geq 54.4542726622231 \wedge x \leq 55.5014702134197$$
$$x \geq 60.7374579694027 \wedge x \leq 61.7846555205993$$
$$x \geq 63.8790506229925 \wedge x \leq 67.0206432765823$$
$$x \geq 68.0678408277789 \wedge x \leq 70.162235930172$$
$$x \geq 71.2094334813686 \wedge x \leq 74.3510261349584$$
$$x \geq 76.4454212373516 \wedge x \leq 77.4926187885482$$
$$x \geq 80.634211442138 \wedge x \leq 82.7286065445312$$
$$x \geq 83.7758040957278 \wedge x \leq 85.870199198121$$
$$x \geq 89.0117918517108 \wedge x \leq 90.0589894029074$$
$$x \geq 92.1533845053006 \wedge x \leq 93.2005820564972$$
$$x \geq 96.342174710087 \wedge x \leq 98.4365698124802$$
$$x \geq 99.4837673636768$$
Solving inequality on a graph