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cos(x)+sqrt((2-sqrt(2))/2)*(sinx+1)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
              ___________                 
             /       ___                  
            /  2 - \/ 2                   
cos(x) +   /   --------- *(sin(x) + 1) = 0
         \/        2                      
$$\sqrt{\frac{2 - \sqrt{2}}{2}} \left(\sin{\left(x \right)} + 1\right) + \cos{\left(x \right)} = 0$$
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      2  
$$x_{1} = - \frac{\pi}{2}$$
           /           ___________\
           |  ___     /       ___ |
           |\/ 2  + \/  2 - \/ 2  |
x2 = 2*atan|----------------------|
           |           ___________|
           |  ___     /       ___ |
           \\/ 2  - \/  2 - \/ 2  /
$$x_{2} = 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{2}} \right)}$$
x2 = 2*atan((sqrt(2 - sqrt(2)) + sqrt(2))/(-sqrt(2 - sqrt(2)) + sqrt(2)))
Suma y producto de raíces [src]
suma
             /           ___________\
             |  ___     /       ___ |
  pi         |\/ 2  + \/  2 - \/ 2  |
- -- + 2*atan|----------------------|
  2          |           ___________|
             |  ___     /       ___ |
             \\/ 2  - \/  2 - \/ 2  /
$$- \frac{\pi}{2} + 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{2}} \right)}$$
=
      /           ___________\     
      |  ___     /       ___ |     
      |\/ 2  + \/  2 - \/ 2  |   pi
2*atan|----------------------| - --
      |           ___________|   2 
      |  ___     /       ___ |     
      \\/ 2  - \/  2 - \/ 2  /     
$$- \frac{\pi}{2} + 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{2}} \right)}$$
producto
           /           ___________\
           |  ___     /       ___ |
-pi        |\/ 2  + \/  2 - \/ 2  |
----*2*atan|----------------------|
 2         |           ___________|
           |  ___     /       ___ |
           \\/ 2  - \/  2 - \/ 2  /
$$- \frac{\pi}{2} \cdot 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{2}} \right)}$$
=
        /           ___________\
        |  ___     /       ___ |
        |\/ 2  + \/  2 - \/ 2  |
-pi*atan|----------------------|
        |           ___________|
        |  ___     /       ___ |
        \\/ 2  - \/  2 - \/ 2  /
$$- \pi \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{2}} \right)}$$
-pi*atan((sqrt(2) + sqrt(2 - sqrt(2)))/(sqrt(2) - sqrt(2 - sqrt(2))))
Respuesta numérica [src]
x1 = 48.6946861306418
x2 = 92.6769832808989
x3 = 86.3937979737193
x4 = -66.552124329879
x5 = -7.85398163397448
x6 = 52.8283965065331
x7 = -430.976872146295
x8 = -64.4026493985908
x9 = -58.1194640914112
x10 = -47.7025684083402
x11 = -83.2522053201295
x12 = -20.4203522483337
x13 = 54.9778714378214
x14 = 15.1292846634556
x15 = -3.72027125808313
x16 = 111.526539202438
x17 = 23.5619449019235
x18 = -45.553093477052
x19 = 8.84609935627604
x20 = 67.5442420521806
x21 = 40.262025892174
x22 = -72.8353096370586
x23 = -51.8362787842316
x24 = 80.1106126665397
x25 = 84.2443230424311
x26 = -39.2699081698724
x27 = 65.3947671208923
x28 = 46.5452111993536
x29 = 4.71238898038469
x30 = 36.1283155162826
x31 = -70.6858347057703
x32 = 71.6779524280719
x33 = -79.1184949442382
x34 = 42.4115008234622
x35 = -35.1361977939811
x36 = -85.4016802514178
x37 = 10.9955742875643
x38 = 98.9601685880785
x39 = 59.1115818137127
x40 = -221.48228207808
x41 = 77.9611377352515
x42 = -22.5698271796219
x43 = 17.2787595947439
x44 = -60.2689390226994
x45 = -95.8185759344887
x46 = 2.56291404909646
x47 = -28.8530124868015
x48 = 27.6956552778148
x49 = 73.8274273593601
x50 = 90.5275083496107
x51 = 61.261056745001
x52 = -26.7035375555132
x53 = -89.5353906273091
x54 = -41.4193831011606
x55 = -32.9867228626928
x56 = -14.1371669411541
x57 = -53.9857537155198
x58 = -76.9690200129499
x59 = 96.8106936567902
x60 = -16.2866418724423
x61 = 21.4124699706352
x62 = -10.0034565652627
x63 = -1.5707963267949
x64 = 29.845130209103
x65 = 33.9788405849944
x66 = -91.6848655585973
x67 = -97.9680508657769
x67 = -97.9680508657769