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sin(x)cos(x)=1/16 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
sin(x)*cos(x) = 1/16
$$\sin{\left(x \right)} \cos{\left(x \right)} = \frac{1}{16}$$
Gráfica
Suma y producto de raíces [src]
suma
      /                    _____________\         /                   _____________\         /                   _____________\         /         _____________          \
      |         ___       /         ___ |         |        ___       /         ___ |         |        ___       /         ___ |         |        /         ___        ___|
2*atan\-8 + 3*\/ 7  + 4*\/  8 - 3*\/ 7  / - 2*atan\8 - 3*\/ 7  + 4*\/  8 - 3*\/ 7  / - 2*atan\8 + 3*\/ 7  + 4*\/  8 + 3*\/ 7  / - 2*atan\8 - 4*\/  8 + 3*\/ 7   + 3*\/ 7 /
$$\left(- 2 \operatorname{atan}{\left(3 \sqrt{7} + 8 + 4 \sqrt{3 \sqrt{7} + 8} \right)} + \left(- 2 \operatorname{atan}{\left(- 3 \sqrt{7} + 4 \sqrt{8 - 3 \sqrt{7}} + 8 \right)} + 2 \operatorname{atan}{\left(-8 + 4 \sqrt{8 - 3 \sqrt{7}} + 3 \sqrt{7} \right)}\right)\right) - 2 \operatorname{atan}{\left(- 4 \sqrt{3 \sqrt{7} + 8} + 3 \sqrt{7} + 8 \right)}$$
=
        /         _____________          \         /                   _____________\         /                   _____________\         /                    _____________\
        |        /         ___        ___|         |        ___       /         ___ |         |        ___       /         ___ |         |         ___       /         ___ |
- 2*atan\8 - 4*\/  8 + 3*\/ 7   + 3*\/ 7 / - 2*atan\8 - 3*\/ 7  + 4*\/  8 - 3*\/ 7  / - 2*atan\8 + 3*\/ 7  + 4*\/  8 + 3*\/ 7  / + 2*atan\-8 + 3*\/ 7  + 4*\/  8 - 3*\/ 7  /
$$- 2 \operatorname{atan}{\left(3 \sqrt{7} + 8 + 4 \sqrt{3 \sqrt{7} + 8} \right)} - 2 \operatorname{atan}{\left(- 3 \sqrt{7} + 4 \sqrt{8 - 3 \sqrt{7}} + 8 \right)} - 2 \operatorname{atan}{\left(- 4 \sqrt{3 \sqrt{7} + 8} + 3 \sqrt{7} + 8 \right)} + 2 \operatorname{atan}{\left(-8 + 4 \sqrt{8 - 3 \sqrt{7}} + 3 \sqrt{7} \right)}$$
producto
      /                    _____________\        /                   _____________\        /                   _____________\        /         _____________          \
      |         ___       /         ___ |        |        ___       /         ___ |        |        ___       /         ___ |        |        /         ___        ___|
2*atan\-8 + 3*\/ 7  + 4*\/  8 - 3*\/ 7  /*-2*atan\8 - 3*\/ 7  + 4*\/  8 - 3*\/ 7  /*-2*atan\8 + 3*\/ 7  + 4*\/  8 + 3*\/ 7  /*-2*atan\8 - 4*\/  8 + 3*\/ 7   + 3*\/ 7 /
$$2 \operatorname{atan}{\left(-8 + 4 \sqrt{8 - 3 \sqrt{7}} + 3 \sqrt{7} \right)} \left(- 2 \operatorname{atan}{\left(- 3 \sqrt{7} + 4 \sqrt{8 - 3 \sqrt{7}} + 8 \right)}\right) \left(- 2 \operatorname{atan}{\left(3 \sqrt{7} + 8 + 4 \sqrt{3 \sqrt{7} + 8} \right)}\right) \left(- 2 \operatorname{atan}{\left(- 4 \sqrt{3 \sqrt{7} + 8} + 3 \sqrt{7} + 8 \right)}\right)$$
=
        /                    _____________\     /         _____________          \     /                   _____________\     /                   _____________\
        |         ___       /         ___ |     |        /         ___        ___|     |        ___       /         ___ |     |        ___       /         ___ |
-16*atan\-8 + 3*\/ 7  + 4*\/  8 - 3*\/ 7  /*atan\8 - 4*\/  8 + 3*\/ 7   + 3*\/ 7 /*atan\8 - 3*\/ 7  + 4*\/  8 - 3*\/ 7  /*atan\8 + 3*\/ 7  + 4*\/  8 + 3*\/ 7  /
$$- 16 \operatorname{atan}{\left(-8 + 4 \sqrt{8 - 3 \sqrt{7}} + 3 \sqrt{7} \right)} \operatorname{atan}{\left(- 3 \sqrt{7} + 4 \sqrt{8 - 3 \sqrt{7}} + 8 \right)} \operatorname{atan}{\left(3 \sqrt{7} + 8 + 4 \sqrt{3 \sqrt{7} + 8} \right)} \operatorname{atan}{\left(- 4 \sqrt{3 \sqrt{7} + 8} + 3 \sqrt{7} + 8 \right)}$$
-16*atan(-8 + 3*sqrt(7) + 4*sqrt(8 - 3*sqrt(7)))*atan(8 - 4*sqrt(8 + 3*sqrt(7)) + 3*sqrt(7))*atan(8 - 3*sqrt(7) + 4*sqrt(8 - 3*sqrt(7)))*atan(8 + 3*sqrt(7) + 4*sqrt(8 + 3*sqrt(7)))
Respuesta rápida [src]
           /                    _____________\
           |         ___       /         ___ |
x1 = 2*atan\-8 + 3*\/ 7  + 4*\/  8 - 3*\/ 7  /
$$x_{1} = 2 \operatorname{atan}{\left(-8 + 4 \sqrt{8 - 3 \sqrt{7}} + 3 \sqrt{7} \right)}$$
            /                   _____________\
            |        ___       /         ___ |
x2 = -2*atan\8 - 3*\/ 7  + 4*\/  8 - 3*\/ 7  /
$$x_{2} = - 2 \operatorname{atan}{\left(- 3 \sqrt{7} + 4 \sqrt{8 - 3 \sqrt{7}} + 8 \right)}$$
            /                   _____________\
            |        ___       /         ___ |
x3 = -2*atan\8 + 3*\/ 7  + 4*\/  8 + 3*\/ 7  /
$$x_{3} = - 2 \operatorname{atan}{\left(3 \sqrt{7} + 8 + 4 \sqrt{3 \sqrt{7} + 8} \right)}$$
            /         _____________          \
            |        /         ___        ___|
x4 = -2*atan\8 - 4*\/  8 + 3*\/ 7   + 3*\/ 7 /
$$x_{4} = - 2 \operatorname{atan}{\left(- 4 \sqrt{3 \sqrt{7} + 8} + 3 \sqrt{7} + 8 \right)}$$
x4 = -2*atan(-4*sqrt(3*sqrt(7) + 8) + 3*sqrt(7) + 8)
Respuesta numérica [src]
x1 = 20.3576883327496
x2 = 44.0449610658411
x3 = 95.7559120189047
x4 = -58.1821280069952
x5 = 50.3281463730207
x6 = -14.1998308567381
x7 = -53.3444111954425
x8 = 37.7617757586615
x9 = 42.3488369078782
x10 = 72.3192949481493
x11 = 92.6143193653149
x12 = 81.7440729089187
x13 = 12.6290345299432
x14 = -81.6187450777506
x15 = 51.7736148686476
x16 = 7.79131771839045
x17 = 0.0626639155840327
x18 = -64.4653133141748
x19 = -50.2028185418527
x20 = -75.335559770571
x21 = 119.443184751996
x22 = 67.4815781365965
x23 = -1708.96373963726
x24 = 22.0538124907126
x25 = -36.1909794318667
x26 = -29.9077941246871
x27 = -94.1851156921098
x28 = 100.593628830457
x29 = 59.7529243337901
x30 = 15.770627183533
x31 = 1.50813241121086
x32 = -100.468300999289
x33 = 14.07450302557
x34 = -87.9019303849302
x35 = -65.9107818098016
x36 = -37.6364479274935
x37 = -95.8812398500727
x38 = -7.91664554955852
x39 = 56.6113316802003
x40 = -80.1732765821238
x41 = -73.8900912749442
x42 = 58.0568001758271
x43 = -97.3267083456996
x44 = -28.2116699667241
x45 = 78.6024802553289
x46 = 18.9122198371228
x47 = 6.34584922276362
x48 = 23.4992809863394
x49 = -15.6452993523649
x50 = 64.3399854830067
x51 = 69.1777022945595
x52 = -59.627596502622
x53 = -17.3414235103279
x54 = -9.36211404518535
x55 = -67.6069059677646
x56 = -83.3148692357136
x57 = 34.6201831050718
x58 = -39.3325720854564
x59 = 88.0272582160982
x60 = -61.323720660585
x61 = -6.22052139159555
x62 = -1086.92839422648
x63 = -42.4741647390462
x64 = 89.4727267117251
x65 = -72.1939671169812
x66 = -51.8989426998156
x67 = -78.4771524241608
x68 = -89.5980545428931
x69 = 70.6231707901863
x70 = -21.9284846595445
x71 = -23.6246088175075
x72 = 36.0656516006986
x73 = 48.6320222150578
x74 = 28.3369977978922
x75 = 73.7647634437761
x76 = -45.615757392636
x77 = -31.3532626203139
x78 = 4.64972506480066
x79 = -43.9196332346731
x80 = -1.63346024237893
x81 = -86.4564618893033
x82 = 66.0361096409697
x83 = 80.0479487509557
x84 = 45.490429561468
x85 = -20.4830161639177
x86 = 26.6408736399292
x87 = 29.782466293519
x88 = 86.3311340581353
x89 = 94.3104435232778
x89 = 94.3104435232778