Sr Examen

tg(ctg(x))=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
tan(cot(x)) = 0
$$\tan{\left(\cot{\left(x \right)} \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$\tan{\left(\cot{\left(x \right)} \right)} = 0$$
cambiamos
$$\tan{\left(\cot{\left(x \right)} \right)} - 1 = 0$$
$$\tan{\left(\cot{\left(x \right)} \right)} - 1 = 0$$
Sustituimos
$$w = \tan{\left(\cot{\left(x \right)} \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = 1$$
Obtenemos la respuesta: w = 1
hacemos cambio inverso
$$\tan{\left(\cot{\left(x \right)} \right)} = w$$
sustituimos w:
Gráfica
Suma y producto de raíces [src]
suma
pi
--
2 
$$\frac{\pi}{2}$$
=
pi
--
2 
$$\frac{\pi}{2}$$
producto
pi
--
2 
$$\frac{\pi}{2}$$
=
pi
--
2 
$$\frac{\pi}{2}$$
pi/2
Respuesta rápida [src]
     pi
x1 = --
     2 
$$x_{1} = \frac{\pi}{2}$$
x1 = pi/2
Respuesta numérica [src]
x1 = -16.016132339065
x2 = 1.5707963267949
x3 = -38.0072809141935
x4 = 14.1371669411541
x5 = -70.6858347057703
x6 = 32.9867228626928
x7 = 61.261056745001
x8 = 28.5825029534241
x9 = -36.1283155162826
x10 = 7.85398163397448
x11 = 34.2493501183717
x12 = 42.4115008234622
x13 = -22.2993176462445
x14 = -93.9396105365778
x15 = -9.73294703188536
x16 = 98.9601685880785
x17 = 83.2522053201295
x18 = -89.5353906273091
x19 = -54.9778714378214
x20 = -67.5442420521806
x21 = -51.8362787842316
x22 = -83.2522053201295
x23 = -14.1371669411541
x24 = 92.6769832808989
x25 = 64.4026493985908
x26 = 48.6946861306418
x27 = 67.5442420521806
x28 = 76.9690200129499
x29 = 66.1312769156738
x30 = 100.222795843757
x31 = -32.9867228626928
x32 = 23.5619449019235
x33 = 10.9955742875643
x34 = -88.0703020968947
x35 = 5.9750162360636
x36 = 56.2404986935003
x37 = -59.9984294893221
x38 = -49.9573133863207
x39 = 16.016132339065
x40 = -80.1106126665397
x41 = -64.4026493985908
x42 = -29.845130209103
x43 = -86.3937979737193
x44 = 4.71238898038469
x45 = 17.2787595947439
x46 = 20.4203522483337
x47 = -76.9690200129499
x48 = -71.9484619614493
x49 = -1.5707963267949
x50 = 21.9593283304909
x51 = 86.3937979737193
x52 = -97.6975413323996
x53 = 39.2699081698724
x54 = -5.9750162360636
x55 = -39.2699081698724
x56 = 36.1283155162826
x57 = -75.706392757271
x58 = 51.8362787842316
x59 = 80.1106126665397
x60 = 43.6741280791411
x61 = -53.7152441821425
x62 = 12.2582015432432
x63 = -92.6769832808989
x64 = 89.5353906273091
x65 = 58.1194640914112
x66 = 49.9573133863207
x67 = 73.8274273593601
x68 = -65.9547238021501
x69 = -58.1194640914112
x70 = 78.2316472686288
x71 = -20.4203522483337
x72 = -44.0352991109468
x73 = 95.8185759344887
x74 = 88.2727633716302
x75 = 54.9778714378214
x76 = -95.8185759344887
x77 = 29.845130209103
x78 = 26.7035375555132
x79 = -23.5619449019235
x80 = -42.4115008234622
x81 = -31.7240956070139
x82 = 38.0072809141935
x83 = 72.2488675327821
x84 = -61.261056745001
x85 = -48.6946861306418
x86 = 70.6858347057703
x87 = -98.9601685880785
x88 = -26.7035375555132
x89 = -10.9955742875643
x90 = -81.9895780644506
x91 = 94.0899484174056
x92 = 45.553093477052
x93 = 59.9984294893221
x94 = -73.8274273593601
x95 = -27.9661648111922
x96 = -4.71238898038469
x97 = -45.553093477052
x98 = -7.85398163397448
x99 = -17.2787595947439
x100 = 81.9895780644506
x100 = 81.9895780644506