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sqr(2)*(sinx+cosx)=(1/sinx)+(1/cosx) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                   2     1        1   
2*(sin(x) + cos(x))  = ------ + ------
                       sin(x)   cos(x)
$$2 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} = \frac{1}{\cos{\left(x \right)}} + \frac{1}{\sin{\left(x \right)}}$$
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Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     -pi 
x1 = ----
      4
$$x_{1} = - \frac{\pi}{4}$$ 
     3*pi
x2 = ----
      4
$$x_{2} = \frac{3 \pi}{4}$$ 
           /       / 6      5       4      3      2             \\
x3 = 2*atan\CRootOf\x  - 4*x  + 11*x  + 8*x  - 5*x  - 4*x + 1, 0//
$$x_{3} = 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - 4 x^{5} + 11 x^{4} + 8 x^{3} - 5 x^{2} - 4 x + 1, 0\right)} \right)}$$ 
           /       / 6      5       4      3      2             \\
x4 = 2*atan\CRootOf\x  - 4*x  + 11*x  + 8*x  - 5*x  - 4*x + 1, 1//
$$x_{4} = 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - 4 x^{5} + 11 x^{4} + 8 x^{3} - 5 x^{2} - 4 x + 1, 1\right)} \right)}$$ 
         /    /       / 6      5       4      3      2             \\\         /    /       / 6      5       4      3      2             \\\
x5 = 2*re\atan\CRootOf\x  - 4*x  + 11*x  + 8*x  - 5*x  - 4*x + 1, 2/// + 2*I*im\atan\CRootOf\x  - 4*x  + 11*x  + 8*x  - 5*x  - 4*x + 1, 2///
$$x_{5} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - 4 x^{5} + 11 x^{4} + 8 x^{3} - 5 x^{2} - 4 x + 1, 2\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - 4 x^{5} + 11 x^{4} + 8 x^{3} - 5 x^{2} - 4 x + 1, 2\right)} \right)}\right)}$$ 
         /    /       / 6      5       4      3      2             \\\         /    /       / 6      5       4      3      2             \\\
x6 = 2*re\atan\CRootOf\x  - 4*x  + 11*x  + 8*x  - 5*x  - 4*x + 1, 3/// + 2*I*im\atan\CRootOf\x  - 4*x  + 11*x  + 8*x  - 5*x  - 4*x + 1, 3///
$$x_{6} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - 4 x^{5} + 11 x^{4} + 8 x^{3} - 5 x^{2} - 4 x + 1, 3\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - 4 x^{5} + 11 x^{4} + 8 x^{3} - 5 x^{2} - 4 x + 1, 3\right)} \right)}\right)}$$ 
         /    /       / 6      5       4      3      2             \\\         /    /       / 6      5       4      3      2             \\\
x7 = 2*re\atan\CRootOf\x  - 4*x  + 11*x  + 8*x  - 5*x  - 4*x + 1, 4/// + 2*I*im\atan\CRootOf\x  - 4*x  + 11*x  + 8*x  - 5*x  - 4*x + 1, 4///
$$x_{7} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - 4 x^{5} + 11 x^{4} + 8 x^{3} - 5 x^{2} - 4 x + 1, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - 4 x^{5} + 11 x^{4} + 8 x^{3} - 5 x^{2} - 4 x + 1, 4\right)} \right)}\right)}$$ 
         /    /       / 6      5       4      3      2             \\\         /    /       / 6      5       4      3      2             \\\
x8 = 2*re\atan\CRootOf\x  - 4*x  + 11*x  + 8*x  - 5*x  - 4*x + 1, 5/// + 2*I*im\atan\CRootOf\x  - 4*x  + 11*x  + 8*x  - 5*x  - 4*x + 1, 5///
$$x_{8} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - 4 x^{5} + 11 x^{4} + 8 x^{3} - 5 x^{2} - 4 x + 1, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - 4 x^{5} + 11 x^{4} + 8 x^{3} - 5 x^{2} - 4 x + 1, 5\right)} \right)}\right)}$$ 
Eq(x8, 2*re(atan(CRootOf(x^6 - 4*x^5 + 11*x^4 + 8*x^3 - 5*x^2 - 4*x + 1, 5))) + 2*i*im(atan(CRootOf(x^6 - 4*x^5 + 11*x^4 + 8*x^3 - 5*x^2 - 4*x + 1, 5))))
Respuesta numérica [src] 
x1 = -110.74114103904
x2 = -38.484510006475
x3 = 1246.42688531175
x4 = 88.3923280889581
x5 = 80.8960108299372
x6 = 44.410030938701
x7 = 30.6305283725005
x8 = 84.037603483527
x9 = 38.1268456315214
x10 = -5.14012276882859
x11 = 36.9137136796801
x12 = 11.7809724509617
x13 = 68.329640215578
x14 = -54.1924732744239
x15 = 70.2581009173264
x16 = -47.9092879672443
x17 = -16.4933614313464
x18 = 90.3207887907066
x19 = 8.63937979737193
x20 = -1712.95339436983
x21 = -69.9004365423729
x22 = -19.6349540849362
x23 = 49.4800842940392
x24 = -93.8200458192499
x25 = -3.92699081698724
x26 = -23.9896786903674
x27 = -76.1836218495525
x28 = -5.85545151873568
x29 = 62.0464549083984
x30 = 107.241884010497
x31 = -32.2013246992954
x32 = -74.255161147804
x33 = 71.4712328691678
x34 = -87.5368605120703
x35 = -1507.53673993466
x36 = 43.1968989868597
x37 = 93.4623814442964
x38 = 63.9749156101469
x39 = 32.5589890742489
x40 = 14.9225651045515
x41 = 1475.76314902381
x42 = 24.3473430653209
x43 = -101.316363078271
x44 = -17.7064933831878
x45 = -100.103231126429
x46 = -43.5545633618132
x47 = 99.7455667514759
x48 = 40.0553063332699
x49 = -25239.127645152
x50 = -13.3517687777566
x51 = 75.8259574745989
x52 = -30.2728639975469
x53 = 58.9048622548086
x54 = -49.8377486689928
x55 = -56.1209339761724
x56 = -7.06858347057703
x57 = 82.1091427817785
x58 = 55.7632696012188
x59 = -79.3252145031423
x60 = -51.0508806208341
x61 = 137.444678594553
x62 = 74.6128255227576
x63 = 18.0641577581413
x64 = -41.6261026600648
x65 = -85.6083998103219
x66 = -35.3429173528852
x67 = 52.621676947629
x68 = 96.6039740978861
x69 = -82.4668071567321
x70 = -63.6172512351933
x71 = -61.6887905334449
x72 = 27.4889357189107
x73 = -10.2101761241668
x74 = -30.988192747454
x75 = 46.3384916404494
x76 = -60.4756585816035
x77 = 19.9926184598898
x78 = -67.9719758406245
x79 = -91.8915851175014
x80 = -98.174770424681
x81 = 5.49778714378214
x82 = -57.3340659280137
x83 = 77.7544181763474
x84 = -25.9181393921158
x85 = 2.35619449019234
x86 = 33.7721210260903
x87 = 26.2758037670693
x87 = 26.2758037670693
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