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ctg3x-ctgx=4cosx la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
cot(3*x) - cot(x) = 4*cos(x)
$$- \cot{\left(x \right)} + \cot{\left(3 x \right)} = 4 \cos{\left(x \right)}$$
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      2  
$$x_{1} = - \frac{\pi}{2}$$
     pi
x2 = --
     2 
$$x_{2} = \frac{\pi}{2}$$
x2 = pi/2
Suma y producto de raíces [src]
suma
  pi   pi
- -- + --
  2    2 
$$- \frac{\pi}{2} + \frac{\pi}{2}$$
=
0
$$0$$
producto
-pi  pi
----*--
 2   2 
$$- \frac{\pi}{2} \frac{\pi}{2}$$
=
   2 
-pi  
-----
  4  
$$- \frac{\pi^{2}}{4}$$
-pi^2/4
Respuesta numérica [src]
x1 = 26.3544717051144
x2 = 35.4301838154849
x3 = 22.165681500328
x4 = -77.6671517137477
x5 = -73.4783615089613
x6 = -21.8166156499291
x7 = 4.01425727958696
x8 = -55.3269372882203
x9 = 47.9965544298441
x10 = -86.3937979737193
x11 = -10.9955742875643
x12 = -28.0998009571087
x13 = -48.6946861306418
x14 = -45.553093477052
x15 = 26.7035375555132
x16 = 8.20304748437335
x17 = 252.898208613978
x18 = 89.1863247769102
x19 = 32.9867228626928
x20 = -35.7792496658838
x21 = -101.403629540871
x22 = -33.6848545634906
x23 = 94.0732466824944
x24 = -98.9601685880785
x25 = -81.8559419185341
x26 = -27.401669256311
x27 = 39.2699081698724
x28 = -58.1194640914112
x29 = 50.0909495322373
x30 = -71.3839664065681
x31 = -39.9680398706701
x32 = -80.1106126665397
x33 = 142.942465738336
x34 = 86.3937979737193
x35 = 45.553093477052
x36 = 51.8362787842316
x37 = 76.9690200129499
x38 = 66.1479786505851
x39 = 91.9788515801012
x40 = -19.7222205475359
x41 = 83.2522053201295
x42 = 16.5806278939461
x43 = -14.1371669411541
x44 = 68.2423737529783
x45 = 72.4311639577647
x46 = -73.8274273593601
x47 = -67.8933079025794
x48 = -69.9877030049726
x49 = -29.845130209103
x50 = 70.3367688553715
x51 = -89.5353906273091
x52 = 64.4026493985908
x53 = -92.6769832808989
x54 = 29.845130209103
x55 = -51.8362787842316
x56 = -67.5442420521806
x57 = -98.6111027376796
x58 = -88.8372589265114
x59 = -83.9503370209273
x60 = 24.2600766027212
x61 = 54.2797397370236
x62 = -7.85398163397448
x63 = -37.873644768277
x64 = -86.0447321233204
x65 = 14.1371669411541
x66 = 80.1106126665397
x67 = 10.2974425867665
x68 = 42.4115008234622
x69 = -26.0054058547155
x70 = 61.9591884457987
x71 = 36.1283155162826
x72 = -1.5707963267949
x73 = -95.8185759344887
x74 = -42.0624349730633
x75 = 212.057504117311
x76 = -23.5619449019235
x77 = 99.6583002888762
x78 = -79.7615468161409
x79 = 6.10865238198015
x80 = -4.71238898038469
x81 = -63.704517697793
x82 = 98.2620368872808
x83 = -65.7989128001862
x84 = 73.8274273593601
x85 = 17.9768912955416
x86 = -61.261056745001
x87 = 58.1194640914112
x88 = 1.5707963267949
x89 = -42.4115008234622
x89 = -42.4115008234622