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sin(x)/(cos(x/2)^(2))=4*sin(x/2)^(2)

sin(x)/(cos(x/2)^(2))=4*sin(x/2)^(2) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
 sin(x)        2/x\
------- = 4*sin |-|
   2/x\         \2/
cos |-|            
    \2/            
$$\frac{\sin{\left(x \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}} = 4 \sin^{2}{\left(\frac{x}{2} \right)}$$
Gráfica
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
     pi
x2 = --
     2 
$$x_{2} = \frac{\pi}{2}$$
x3 = 2*pi
$$x_{3} = 2 \pi$$
x3 = 2*pi
Suma y producto de raíces [src]
suma
pi       
-- + 2*pi
2        
$$\frac{\pi}{2} + 2 \pi$$
=
5*pi
----
 2  
$$\frac{5 \pi}{2}$$
producto
  pi     
0*--*2*pi
  2      
$$2 \pi 0 \frac{\pi}{2}$$
=
0
$$0$$
0
Respuesta numérica [src]
x1 = -73.8274272637031
x2 = -29.8451300609921
x3 = -62.8318530717959
x4 = -42.4115004122626
x5 = 58.1194650696688
x6 = 18.8495559215388
x7 = -87.9645943005142
x8 = 56.5486677646163
x9 = 95.8185761036174
x10 = 69.1150383789755
x11 = -86.3937975843584
x12 = 7.85398177153197
x13 = 94.2477796076938
x14 = 39.2699091444638
x15 = 100.530964914873
x16 = -36.1283153942839
x17 = 20.4203521697366
x18 = 12.5663706143592
x19 = -94.2477796076938
x20 = -4.7123880493521
x21 = 37.6991118430775
x22 = -50.2654824574367
x23 = 81.6814089933346
x24 = 25.1327412287183
x25 = 45.5530939340473
x26 = -67.5442421402238
x27 = -18.8495559215388
x28 = -81.6814089933346
x29 = 83.2522063404359
x30 = 0.0
x31 = 1.57079676052624
x32 = -12.5663706143592
x33 = 75.398223686155
x34 = 50.2654824574367
x35 = 51.8362789374782
x36 = -92.6769824311273
x37 = 89.5353911083419
x38 = 62.8318530717959
x39 = -6.28318530717959
x40 = -17.2787596893022
x41 = -69.1150383789755
x42 = 6.28318530717959
x43 = 43.9822971502571
x44 = -43.9822971502571
x45 = -25.1327412287183
x46 = -61.2610568327732
x47 = -75.398223686155
x48 = 87.9645943005142
x49 = 14.1371671902159
x50 = -56.5486677646163
x51 = 26.7035374558547
x52 = 31.4159265358979
x53 = -23.5619449854602
x54 = -80.1106125600474
x55 = 70.6858346023605
x56 = 64.4026493253831
x57 = -48.6946852411685
x58 = -37.6991118430775
x59 = -31.4159265358979
x59 = -31.4159265358979
Gráfico
sin(x)/(cos(x/2)^(2))=4*sin(x/2)^(2) la ecuación