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sin6x+√3cos6x=-2cos8x.

sin6x+√3cos6x=-2cos8x. equation

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Numerical solution:

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The solution

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sin(6*x) + \/ 3*cos(6*x)  = -2*cos(8*x)
$$\sqrt{3 \cos{\left(6 x \right)}} + \sin{\left(6 x \right)} = - 2 \cos{\left(8 x \right)}$$
The graph
Numerical answer [src]
x1 = 100.328977207775
x2 = -73.6595173842519 - 0.0699811629230317*i
x3 = -67.9387742712195 + 0.0692777784720477*i
x4 = 85.9992657546804 + 0.0692777784720477*i
x5 = 50.0634947503387
x6 = -81.8833967004327
x7 = 26.3090053364743 + 0.0692777784720477*i
x8 = -17.6732918137828 + 0.0692777784720477*i
x9 = 14.3050769162623 + 0.0699811629230317*i
x10 = -61.6555889640399 + 0.0692777784720477*i
x11 = -35.9604055411744 + 0.0699811629230317*i
x12 = -29.6772202339948 + 0.0699811629230317*i
x13 = 94.0457919005958
x14 = 4.31785676134574 + 0.0692777784720477*i
x15 = -19.9353613571254
x16 = 74.3124182505684
x17 = 20.0258200292947 + 0.0692777784720477*i
x18 = -57.951554116303 + 0.0699811629230317*i
x19 = 24.0469357931317
x20 = 92.2824510618599 - 0.0692777784720477*i
x21 = 70.2913024867314 + 0.0692777784720477*i
x22 = -1.96532854583385 + 0.0692777784720477*i
x23 = 46.0380843682603
x24 = 58.2873740665194 + 0.0699811629230317*i
x25 = 64.0081171795518 + 0.0692777784720477*i
x26 = -7.68607165886627 + 0.0699811629230317*i
x27 = 72.0546433254672
x28 = 30.3301211003113
x29 = -41.9265099322539
x30 = -15.909950975047
x31 = 36.2962254913908 + 0.0699811629230317*i
x32 = -45.947625696091 + 0.0692777784720477*i
x33 = 68.0292329433888
x34 = -39.6644403889114 + 0.0692777784720477*i
x35 = 6.08119760008155
x36 = -13.9692569660459 - 0.0699811629230317*i
x37 = -83.6467375391685 + 0.0692777784720477*i
x38 = 52.3212696754399
x39 = 28.0723461752101
x40 = 48.3001539116028 - 0.0692777784720477*i
x41 = 8.33897252518278
x42 = -79.9427026914315 + 0.0699811629230317*i
x43 = -63.9176585073825
x44 = 2.05578721800319
x45 = 42.0169686044233 + 0.0692777784720477*i
x46 = -89.9299228463481 + 0.0692777784720477*i
x47 = -37.9010995501756
x48 = -85.908807082511
x49 = -23.9564771209624 + 0.0692777784720477*i
x50 = -59.8922481253041
x51 = -95.6506659593805 + 0.0699811629230317*i
x52 = 90.0203815185174
x53 = 96.303566825697
x54 = -51.6683688091234 - 0.0699811629230317*i
x55 = 80.2785226416479 + 0.0699811629230317*i
x55 = 80.2785226416479 + 0.0699811629230317*i
The graph
sin6x+√3cos6x=-2cos8x. equation