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sinx+cosx=1/sqrt(2) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
                    1  
sin(x) + cos(x) = -----
                    ___
                  \/ 2 
$$\sin{\left(x \right)} + \cos{\left(x \right)} = \frac{1}{\sqrt{2}}$$
Gráfica
Suma y producto de raíces [src]
suma
        /       ___     ___     ___\         /      ___     ___     ___\
- 2*atan\-2 + \/ 2  + \/ 3  - \/ 6 / + 2*atan\2 + \/ 3  - \/ 2  - \/ 6 /
$$2 \operatorname{atan}{\left(- \sqrt{6} - \sqrt{2} + \sqrt{3} + 2 \right)} - 2 \operatorname{atan}{\left(- \sqrt{6} - 2 + \sqrt{2} + \sqrt{3} \right)}$$
=
        /       ___     ___     ___\         /      ___     ___     ___\
- 2*atan\-2 + \/ 2  + \/ 3  - \/ 6 / + 2*atan\2 + \/ 3  - \/ 2  - \/ 6 /
$$2 \operatorname{atan}{\left(- \sqrt{6} - \sqrt{2} + \sqrt{3} + 2 \right)} - 2 \operatorname{atan}{\left(- \sqrt{6} - 2 + \sqrt{2} + \sqrt{3} \right)}$$
producto
       /       ___     ___     ___\       /      ___     ___     ___\
-2*atan\-2 + \/ 2  + \/ 3  - \/ 6 /*2*atan\2 + \/ 3  - \/ 2  - \/ 6 /
$$- 2 \operatorname{atan}{\left(- \sqrt{6} - 2 + \sqrt{2} + \sqrt{3} \right)} 2 \operatorname{atan}{\left(- \sqrt{6} - \sqrt{2} + \sqrt{3} + 2 \right)}$$
=
       /       ___     ___     ___\     /      ___     ___     ___\
-4*atan\-2 + \/ 2  + \/ 3  - \/ 6 /*atan\2 + \/ 3  - \/ 2  - \/ 6 /
$$- 4 \operatorname{atan}{\left(- \sqrt{6} - 2 + \sqrt{2} + \sqrt{3} \right)} \operatorname{atan}{\left(- \sqrt{6} - \sqrt{2} + \sqrt{3} + 2 \right)}$$
-4*atan(-2 + sqrt(2) + sqrt(3) - sqrt(6))*atan(2 + sqrt(3) - sqrt(2) - sqrt(6))
Respuesta rápida [src]
            /       ___     ___     ___\
x1 = -2*atan\-2 + \/ 2  + \/ 3  - \/ 6 /
$$x_{1} = - 2 \operatorname{atan}{\left(- \sqrt{6} - 2 + \sqrt{2} + \sqrt{3} \right)}$$
           /      ___     ___     ___\
x2 = 2*atan\2 + \/ 3  - \/ 2  - \/ 6 /
$$x_{2} = 2 \operatorname{atan}{\left(- \sqrt{6} - \sqrt{2} + \sqrt{3} + 2 \right)}$$
x2 = 2*atan(-sqrt(6) - sqrt(2) + sqrt(3) + 2)
Respuesta numérica [src]
x1 = 26.9653369433124
x2 = 77.2308194007491
x3 = -100.792764302673
x4 = -94.5095789954929
x5 = -63.093652459595
x6 = 45.8148928648512
x7 = -37.9609112308767
x8 = 89.7971900151083
x9 = -50.5272818452358
x10 = 93.9859802198946
x11 = 43.720497762458
x12 = 58.3812634792103
x13 = -79.8488132787406
x14 = -17.0169602069447
x15 = 52.0980781720307
x16 = 87.7027949127151
x17 = -98.6983692002793
x18 = 18.5877565337396
x19 = 70.9476340935695
x20 = 50.0036830696375
x21 = -56.8104671524154
x22 = -48.4328867428426
x23 = -10.7337748997651
x24 = 100.269165527074
x25 = 8.11578102177363
x26 = -73.565627971561
x27 = -69.3768377667746
x28 = -86.1319985859202
x29 = -19.1113553093379
x30 = 37.4373124552784
x31 = 24.8709418409192
x32 = -339.553805975497
x33 = -4.45058959258554
x34 = 75.1364242983559
x35 = -67.2824426643814
x36 = -12.8281700021583
x37 = -29.5833308213039
x38 = -326.987435361138
x39 = 96.0803753222878
x40 = -75.6600230739542
x41 = -25.3945406165175
x42 = -88.2263936883134
x43 = 33.248522250492
x44 = -23.3001455141243
x45 = 14.3989663289532
x46 = 64.6644487863899
x47 = -44.2440965380563
x48 = 39.5317075576716
x49 = 6.02138591938044
x50 = 68.8532389911763
x51 = 1.83259571459405
x52 = -0.261799387799149
x53 = -6.54498469497874
x54 = -31.6777259236971
x55 = 56.2868683768171
x56 = -54.7160720500222
x57 = 12.30457122656
x58 = -92.4151838930998
x59 = 144.251462677331
x60 = -42.1497014356631
x61 = 20.6821516361328
x62 = -60.9992573572018
x63 = 62.5700536839967
x64 = -81.9432083811338
x65 = 1212.39296489786
x66 = -35.8665161284835
x67 = 83.5140047079287
x68 = 81.4196096055355
x69 = 31.1541271480988
x69 = 31.1541271480988