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(tg(x)/cos(x))+(1/(1+sin(x)))=4/3 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
tan(x)       1           
------ + ---------- = 4/3
cos(x)   1 + sin(x)      
$$\frac{\tan{\left(x \right)}}{\cos{\left(x \right)}} + \frac{1}{\sin{\left(x \right)} + 1} = \frac{4}{3}$$
Gráfica
Respuesta rápida [src]
     -5*pi
x1 = -----
       6  
$$x_{1} = - \frac{5 \pi}{6}$$
     -pi 
x2 = ----
      6  
$$x_{2} = - \frac{\pi}{6}$$
     pi
x3 = --
     6 
$$x_{3} = \frac{\pi}{6}$$
     5*pi
x4 = ----
      6  
$$x_{4} = \frac{5 \pi}{6}$$
x4 = 5*pi/6
Suma y producto de raíces [src]
suma
  5*pi   pi   pi   5*pi
- ---- - -- + -- + ----
   6     6    6     6  
$$\left(\left(- \frac{5 \pi}{6} - \frac{\pi}{6}\right) + \frac{\pi}{6}\right) + \frac{5 \pi}{6}$$
=
0
$$0$$
producto
-5*pi -pi  pi 5*pi
-----*----*--*----
  6    6   6   6  
$$\frac{5 \pi}{6} \frac{\pi}{6} \cdot - \frac{5 \pi}{6} \left(- \frac{\pi}{6}\right)$$
=
     4
25*pi 
------
 1296 
$$\frac{25 \pi^{4}}{1296}$$
25*pi^4/1296
Respuesta numérica [src]
x1 = 9.94837673636768
x2 = -31.9395253114962
x3 = -25.6563400043166
x4 = -16.2315620435473
x5 = 84.2994028713261
x6 = -90.5825881785057
x7 = 22.5147473507269
x8 = -46.6002910282486
x9 = -82.2050077689329
x10 = 88.4881930761125
x11 = 44.5058959258554
x12 = 71.733032256967
x13 = 19.3731546971371
x14 = -40.317105721069
x15 = 81.1578102177363
x16 = -85.3466004225227
x17 = -93.7241808320955
x18 = -18.3259571459405
x19 = 25.6563400043166
x20 = -41.3643032722656
x21 = -27.7507351067098
x22 = 18.3259571459405
x23 = 16.2315620435473
x24 = 63.3554518473942
x25 = -91.6297857297023
x26 = 24.60914245312
x27 = -47.6474885794452
x28 = -57.0722665402146
x29 = 66.497044500984
x30 = 62.3082542961976
x31 = 46.6002910282486
x32 = 5.75958653158129
x33 = -8.90117918517108
x34 = -65.4498469497874
x35 = -74.8746249105567
x36 = 91.6297857297023
x37 = -35.081117965086
x38 = -5.75958653158129
x39 = -96.8657734856853
x40 = 53.9306738866248
x41 = -21.4675497995303
x42 = -100.007366139275
x43 = -69.6386371545737
x44 = 27.7507351067098
x45 = -75.9218224617533
x46 = -56.025068989018
x47 = -60.2138591938044
x48 = 60.2138591938044
x49 = 82.2050077689329
x50 = 90.5825881785057
x51 = -52.8834763354282
x52 = -38.2227106186758
x53 = -87.4409955249159
x54 = 52.8834763354282
x55 = 38.2227106186758
x56 = 31.9395253114962
x57 = 34.0339204138894
x58 = -78.0162175641465
x59 = 13.0899693899575
x60 = -19.3731546971371
x61 = 69.6386371545737
x62 = -34.0339204138894
x63 = -97.9129710368819
x64 = -30.8923277602996
x65 = 97.9129710368819
x66 = -12.0427718387609
x67 = -53.9306738866248
x68 = 8.90117918517108
x69 = 3.66519142918809
x70 = -71.733032256967
x71 = 30.8923277602996
x72 = 47.6474885794452
x73 = 59.1666616426078
x74 = 49.7418836818384
x75 = 74.8746249105567
x76 = 78.0162175641465
x77 = 2.61799387799149
x78 = -3.66519142918809
x79 = 85.3466004225227
x80 = -84.2994028713261
x81 = 40.317105721069
x82 = -24.60914245312
x83 = 12.0427718387609
x84 = 0.523598775598299
x85 = -79.0634151153431
x86 = -9.94837673636768
x87 = -68.5914396033772
x88 = 100.007366139275
x89 = -13.0899693899575
x90 = 56.025068989018
x91 = -63.3554518473942
x92 = -43.4586983746588
x93 = -49.7418836818384
x94 = -2.61799387799149
x95 = -62.3082542961976
x96 = 68.5914396033772
x97 = 75.9218224617533
x98 = 96.8657734856853
x99 = 41.3643032722656
x99 = 41.3643032722656