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√3ctg(x)=1 equation

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Numerical solution:

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The solution

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\/ 3*cot(x)  = 1
3cot⁡(x)=1\sqrt{3 \cot{\left(x \right)}} = 1
Simplify
Detail solution
Given the equation
3cot⁡(x)=1\sqrt{3 \cot{\left(x \right)}} = 1
transform
3cot⁡(x)−1=0\sqrt{3} \sqrt{\cot{\left(x \right)}} - 1 = 0
3cot⁡(x)−1=0\sqrt{3 \cot{\left(x \right)}} - 1 = 0
Do replacement
w=cot⁡(x)w = \cot{\left(x \right)}
Given the equation
3w−1=0\sqrt{3} \sqrt{w} - 1 = 0
Because equation degree is equal to = 1/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2-th degree:
We get:
(3w)2=12\left(\sqrt{3 w}\right)^{2} = 1^{2}
or
3w=13 w = 1
Divide both parts of the equation by 3
w = 1 / (3)

We get the answer: w = 1/3

The final answer:
w1=13w_{1} = \frac{1}{3}
do backward replacement
cot⁡(x)=w\cot{\left(x \right)} = w
substitute w:
The graph
0-80-60-40-2020406080-1001000400
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = acot(1/3)
x1=acot⁡(13)x_{1} = \operatorname{acot}{\left(\frac{1}{3} \right)} 
x1 = acot(1/3)
Sum and product of roots [src] 
sum
acot(1/3)
acot⁡(13)\operatorname{acot}{\left(\frac{1}{3} \right)} 
=
acot(1/3)
acot⁡(13)\operatorname{acot}{\left(\frac{1}{3} \right)} 
product
acot(1/3)
acot⁡(13)\operatorname{acot}{\left(\frac{1}{3} \right)} 
=
acot(1/3)
acot⁡(13)\operatorname{acot}{\left(\frac{1}{3} \right)} 
acot(1/3)
Numerical answer [src] 
x1 = -64.7243999529874
x2 = -39.5916587242691
x3 = 45.2313429226554
x4 = 79.7888621121431
x5 = 70.3640841513737
x6 = -33.3084734170895
x7 = -17.6005101491405
x8 = 67.2224914977839
x9 = -77.2907705673466
x10 = -5.03413953478133
x11 = -61.5828072993976
x12 = -99.2819191424751
x13 = -86.715548528116
x14 = 86.0720474193227
x15 = -42.7332513778588
x16 = -83.5739558745262
x17 = 98.6384180336818
x18 = 57.7977135370145
x19 = 7.53223107957784
x20 = -74.1491779137568
x21 = 82.9304547657329
x22 = -49.0164366850384
x23 = -71.007585260167
x24 = 92.3552327265023
x25 = 48.3729355762452
x26 = 54.6561208834247
x27 = 1.24904577239825
x28 = -30.1668807634997
x29 = 42.0897502690656
x30 = -92.9987338352955
x31 = -55.299621992218
x32 = 38.9481576154758
x33 = -96.1403264888853
x34 = -52.1580293386282
x35 = 89.2136400729125
x36 = 26.3817870011166
x37 = -45.8748440314486
x38 = -67.8659926065772
x39 = -23.8836954563201
x40 = 10.6738237331676
x41 = 4.39063842598805
x42 = -36.4500660706793
x43 = 16.9570090403472
x44 = -20.7421028027303
x45 = 64.0808988441941
x46 = -1.89254688119154
x47 = 51.5145282298349
x48 = -89.8571411817058
x49 = -11.3173248419609
x50 = 32.6649723082962
x51 = -80.4323632209364
x52 = -8.17573218837112
x53 = 73.5056768049635
x54 = 23.2401943475268
x55 = -58.4412146458078
x56 = 76.6472694585533
x57 = -14.4589174955507
x58 = -27.0252881099099
x59 = 95.496825380092
x60 = 29.5233796547064
x61 = 60.9393061906043
x62 = 35.806564961886
x63 = 20.098601693937
x64 = 13.8154163867574
x64 = 13.8154163867574
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