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2*sin(x)-cos(x)=sqrt(3)*sin(x) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
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2*sin(x) - cos(x) = \/ 3 *sin(x)
$$2 \sin{\left(x \right)} - \cos{\left(x \right)} = \sqrt{3} \sin{\left(x \right)}$$
Gráfica
Respuesta rápida [src]
           /                  ___________\
           |       ___       /       ___ |
x1 = 2*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  /
$$x_{1} = 2 \operatorname{atan}{\left(-2 + 2 \sqrt{2 - \sqrt{3}} + \sqrt{3} \right)}$$
            /                 ___________\
            |      ___       /       ___ |
x2 = -2*atan\2 - \/ 3  + 2*\/  2 - \/ 3  /
$$x_{2} = - 2 \operatorname{atan}{\left(- \sqrt{3} + 2 \sqrt{2 - \sqrt{3}} + 2 \right)}$$
x2 = -2*atan(-sqrt(3) + 2*sqrt(2 - sqrt(3)) + 2)
Suma y producto de raíces [src]
suma
      /                  ___________\         /                 ___________\
      |       ___       /       ___ |         |      ___       /       ___ |
2*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  / - 2*atan\2 - \/ 3  + 2*\/  2 - \/ 3  /
$$- 2 \operatorname{atan}{\left(- \sqrt{3} + 2 \sqrt{2 - \sqrt{3}} + 2 \right)} + 2 \operatorname{atan}{\left(-2 + 2 \sqrt{2 - \sqrt{3}} + \sqrt{3} \right)}$$
=
        /                 ___________\         /                  ___________\
        |      ___       /       ___ |         |       ___       /       ___ |
- 2*atan\2 - \/ 3  + 2*\/  2 - \/ 3  / + 2*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  /
$$- 2 \operatorname{atan}{\left(- \sqrt{3} + 2 \sqrt{2 - \sqrt{3}} + 2 \right)} + 2 \operatorname{atan}{\left(-2 + 2 \sqrt{2 - \sqrt{3}} + \sqrt{3} \right)}$$
producto
      /                  ___________\        /                 ___________\
      |       ___       /       ___ |        |      ___       /       ___ |
2*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  /*-2*atan\2 - \/ 3  + 2*\/  2 - \/ 3  /
$$2 \operatorname{atan}{\left(-2 + 2 \sqrt{2 - \sqrt{3}} + \sqrt{3} \right)} \left(- 2 \operatorname{atan}{\left(- \sqrt{3} + 2 \sqrt{2 - \sqrt{3}} + 2 \right)}\right)$$
=
       /                  ___________\     /                 ___________\
       |       ___       /       ___ |     |      ___       /       ___ |
-4*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  /*atan\2 - \/ 3  + 2*\/  2 - \/ 3  /
$$- 4 \operatorname{atan}{\left(-2 + 2 \sqrt{2 - \sqrt{3}} + \sqrt{3} \right)} \operatorname{atan}{\left(- \sqrt{3} + 2 \sqrt{2 - \sqrt{3}} + 2 \right)}$$
-4*atan(-2 + sqrt(3) + 2*sqrt(2 - sqrt(3)))*atan(2 - sqrt(3) + 2*sqrt(2 - sqrt(3)))
Respuesta numérica [src]
x1 = 54.7160720500222
x2 = -80.3724120543389
x3 = 32.7249234748937
x4 = -58.3812634792103
x5 = -64.6644487863899
x6 = -92.9387826686981
x7 = 17.0169602069447
x8 = 20.1585528605345
x9 = 45.2912940892529
x10 = -1.83259571459405
x11 = 70.4240353179712
x12 = -45.8148928648512
x13 = -33.248522250492
x14 = -39.5317075576716
x15 = -102.363560629467
x16 = 98.6983692002793
x17 = 42.1497014356631
x18 = -83.5140047079287
x19 = -26.9653369433124
x20 = -36.3901149040818
x21 = -48.9564855184409
x22 = -77.2308194007491
x23 = -42.6733002112614
x24 = 1.30899693899575
x25 = -70.9476340935695
x26 = -86.6555973615185
x27 = 57.857664703612
x28 = -20.6821516361328
x29 = 73.565627971561
x30 = 1240311.51341215
x31 = -17.540558982543
x32 = -61.5228561328001
x33 = 92.4151838930998
x34 = -99.2219679758776
x35 = 89.27359123951
x36 = 23.3001455141243
x37 = -11.2573736753634
x38 = 10.7337748997651
x39 = -114.929931243827
x40 = 82.9904059323304
x41 = 48.4328867428426
x42 = 60.9992573572018
x43 = -89.7971900151083
x44 = 7.59218224617533
x45 = 35.8665161284835
x46 = 29.5833308213039
x47 = 64.1408500107916
x48 = -14.3989663289532
x49 = -4.97418836818384
x50 = -55.2396708256205
x51 = 111.264739814639
x52 = -67.8060414399797
x53 = -30.1069295969022
x54 = -23.8237442897226
x55 = 13.8753675533549
x56 = -96.0803753222878
x57 = 4.45058959258554
x58 = 51.5744793964324
x59 = -74.0892267471593
x60 = 86.1319985859202
x61 = -8.11578102177363
x62 = 95.5567765466895
x63 = -52.0980781720307
x64 = 79.8488132787406
x65 = 76.7072206251508
x66 = 39.0081087820733
x67 = 26.4417381677141
x68 = 67.2824426643814
x68 = 67.2824426643814