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cot(pi/4-x/2)=-1 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Solución numérica:

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Solución

Ha introducido [src]
   /pi   x\     
cot|-- - -| = -1
   \4    2/     
$$\cot{\left(- \frac{x}{2} + \frac{\pi}{4} \right)} = -1$$
Gráfica
Respuesta rápida [src]
x1 = -pi
$$x_{1} = - \pi$$
x1 = -pi
Suma y producto de raíces [src]
suma
-pi
$$- \pi$$
=
-pi
$$- \pi$$
producto
-pi
$$- \pi$$
=
-pi
$$- \pi$$
-pi
Respuesta numérica [src]
x1 = -53.4070751110265
x2 = -59.6902604182061
x3 = -15.707963267949
x4 = 3.14159265358979
x5 = 84.8230016469244
x6 = 21.9911485751286
x7 = 40.8407044966673
x8 = -78.5398163397448
x9 = -21.9911485751286
x10 = 47.1238898038469
x11 = 91.106186954104
x12 = 28.2743338823081
x13 = 34.5575191894877
x14 = 78.5398163397448
x15 = 72.2566310325652
x16 = 15.707963267949
x17 = -47.1238898038469
x18 = -3.14159265358979
x19 = -40.8407044966673
x20 = 53.4070751110265
x21 = -28.2743338823081
x22 = -103.672557568463
x23 = -9.42477796076938
x24 = -97.3893722612836
x25 = 59.6902604182061
x26 = 97.3893722612836
x27 = -72.2566310325652
x28 = -91.106186954104
x29 = 9.42477796076938
x30 = 65.9734457253857
x31 = -65.9734457253857
x32 = -84.8230016469244
x33 = -34.5575191894877
x33 = -34.5575191894877