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2-2*cos(2*x+1)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
2 - 2*cos(2*x + 1) = 0
$$2 - 2 \cos{\left(2 x + 1 \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$2 - 2 \cos{\left(2 x + 1 \right)} = 0$$
es la ecuación trigonométrica más simple
Transportemos 2 al miembro derecho de la ecuación

cambiando el signo de 2

Obtenemos:
$$- 2 \cos{\left(2 x + 1 \right)} = -2$$
Dividamos ambos miembros de la ecuación en -2

La ecuación se convierte en
$$\cos{\left(2 x + 1 \right)} = 1$$
Esta ecuación se reorganiza en
$$2 x + 1 = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$2 x + 1 = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
O
$$2 x + 1 = \pi n$$
$$2 x + 1 = \pi n - \pi$$
, donde n es cualquier número entero
Transportemos
$$1$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$2 x = \pi n - 1$$
$$2 x = \pi n - \pi - 1$$
Dividamos ambos miembros de la ecuación obtenida en
$$2$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{2} - \frac{1}{2}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{2} - \frac{1}{2}$$
Gráfica
Respuesta rápida [src]
x1 = -1/2
$$x_{1} = - \frac{1}{2}$$
x2 = -1/2 + pi
$$x_{2} = - \frac{1}{2} + \pi$$
x2 = -1/2 + pi
Suma y producto de raíces [src]
suma
-1/2 + -1/2 + pi
$$- \frac{1}{2} + \left(- \frac{1}{2} + \pi\right)$$
=
-1 + pi
$$-1 + \pi$$
producto
-(-1/2 + pi) 
-------------
      2      
$$- \frac{- \frac{1}{2} + \pi}{2}$$
=
1   pi
- - --
4   2 
$$\frac{1}{4} - \frac{\pi}{2}$$
1/4 - pi/2
Respuesta numérica [src]
x1 = 40.3407044393771
x2 = -50.7654825719977
x3 = 74.8982234626387
x4 = 56.0486676682168
x5 = -19.3495561143945
x6 = -16.2079631308553
x7 = 30.9159262870104
x8 = 74.898223438543
x9 = 52.9070749300895
x10 = 2.64159246369589
x11 = 81.181409231569
x12 = -79.0398165896957
x13 = -66.4734458198096
x14 = -28.774334009361
x15 = -72.7566307807754
x16 = 37.1991116844333
x17 = 8.92477771141764
x18 = 24.6327410418435
x19 = -41.3407046924268
x20 = 68.6150381983072
x21 = -22.4911483409
x22 = -13.0663706890271
x23 = 59.190260659024
x24 = -85.3230018483134
x25 = -25.6327413004236
x26 = 84.3230015996854
x27 = -57.0486680146157
x28 = -94.7477796937102
x29 = 87.4645945436738
x30 = -66.4734454952564
x31 = -60.1902602894068
x32 = 96.8893719912348
x33 = 62.3318526246625
x34 = -44.4822969180418
x35 = -38.1991117100931
x36 = 37.1991120862432
x37 = 15.2079631189437
x38 = -0.499999763832236
x39 = -69.6150384599139
x40 = -35.0575194394
x41 = -94.7477793547312
x42 = 8.92477785398489
x43 = 52.9070748627202
x44 = 46.6238896200475
x45 = 59.1902602507112
x46 = -44.482297315673
x47 = -57.0486677835605
x48 = -35.0575192349667
x49 = -79.0398163345533
x50 = -72.756631133487
x51 = -50.7654822069915
x52 = -3.64159272057004
x53 = 96.8893720144752
x54 = 34.0575190554025
x55 = 93.7477797642752
x56 = 90.6061873190565
x57 = 30.9159263937849
x58 = -97.8893717847391
x59 = 12.0663704230071
x60 = 100.030964866458
x61 = 81.1814088177103
x62 = -13.066370864054
x63 = 65.4734459669148
x64 = -91.6061870395579
x65 = -57.0486679623631
x66 = -101.03096488771
x67 = 43.4822973900765
x68 = 90.6061867766218
x69 = -63.3318532704001
x70 = -88.4645940725427
x71 = 21.4911488131604
x72 = 78.039816270482
x73 = 15.2079635132397
x74 = 18.3495558593617
x75 = -82.1814088687997
x76 = -28.7743336333882
x77 = -9.92477824950652
x78 = 62.3318530194825
x79 = -6.7831850599744
x80 = 49.7654826064271
x81 = -6.78318544568241
x82 = 71.7566311853842
x83 = -47.6238898802035
x84 = 27.7743340274027
x85 = 5.78318544830917
x85 = 5.78318544830917