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Equation:
Equation tan(x)=0
Equation -x-2+3(x-3)=3(4-x)-3
Equation 4x=24+x
Equation x+3=-9x
Express {x} in terms of y where:
17*x-18*y=10
-12*x-3*y=-9
4*x+16*y=6
4*x-15*y=19
Identical expressions
cos^ two (two x)+cos^2(4x)= one +ctg(6x)
co sinus of e of squared (2x) plus co sinus of e of squared (4x) equally 1 plus ctg(6x)
co sinus of e of to the power of two (two x) plus co sinus of e of squared (4x) equally one plus ctg(6x)
cos2(2x)+cos2(4x)=1+ctg(6x)
cos22x+cos24x=1+ctg6x
cos²(2x)+cos²(4x)=1+ctg(6x)
cos to the power of 2(2x)+cos to the power of 2(4x)=1+ctg(6x)
cos^22x+cos^24x=1+ctg6x
Similar expressions
cos^2(2x)+cos^2(4x)=1-ctg(6x)
cos^2(2x)-cos^2(4x)=1+ctg(6x)

cos^2(2x)+cos^2(4x)=1+ctg(6x) equation

The teacher will be very surprised to see your correct solution 😉

The solution

You have entered [src]

   2           2                    
cos (2*x) + cos (4*x) = 1 + cot(6*x)

$$\cos^{2}{\left(2 x \right)} + \cos^{2}{\left(4 x \right)} = \cot{\left(6 x \right)} + 1$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

     -11*pi
x1 = ------
       12

$$x_{1} = - \frac{11 \pi}{12}$$

     -3*pi
x2 = -----
       4

$$x_{2} = - \frac{3 \pi}{4}$$

     -7*pi
x3 = -----
       12

$$x_{3} = - \frac{7 \pi}{12}$$

     -5*pi
x4 = -----
       12

$$x_{4} = - \frac{5 \pi}{12}$$

     -pi 
x5 = ----
      4

$$x_{5} = - \frac{\pi}{4}$$

     -pi 
x6 = ----
      12

$$x_{6} = - \frac{\pi}{12}$$

     pi
x7 = --
     12

$$x_{7} = \frac{\pi}{12}$$

     pi
x8 = --
     4

$$x_{8} = \frac{\pi}{4}$$

     5*pi
x9 = ----
      12

$$x_{9} = \frac{5 \pi}{12}$$

      7*pi
x10 = ----
       12

$$x_{10} = \frac{7 \pi}{12}$$

      3*pi
x11 = ----
       4

$$x_{11} = \frac{3 \pi}{4}$$

      11*pi
x12 = -----
        12

$$x_{12} = \frac{11 \pi}{12}$$

x12 = 11*pi/12

Sum and product of roots [src]

sum

  11*pi   3*pi   7*pi   5*pi   pi   pi   pi   pi   5*pi   7*pi   3*pi   11*pi
- ----- - ---- - ---- - ---- - -- - -- + -- + -- + ---- + ---- + ---- + -----
    12     4      12     12    4    12   12   4     12     12     4       12

$$\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(- \frac{11 \pi}{12} - \frac{3 \pi}{4}\right) - \frac{7 \pi}{12}\right) - \frac{5 \pi}{12}\right) - \frac{\pi}{4}\right) - \frac{\pi}{12}\right) + \frac{\pi}{12}\right) + \frac{\pi}{4}\right) + \frac{5 \pi}{12}\right) + \frac{7 \pi}{12}\right) + \frac{3 \pi}{4}\right) + \frac{11 \pi}{12}$$

$$0$$

product

-11*pi -3*pi -7*pi -5*pi -pi  -pi  pi pi 5*pi 7*pi 3*pi 11*pi
------*-----*-----*-----*----*----*--*--*----*----*----*-----
  12     4     12    12   4    12  12 4   12   12   4     12

$$\frac{11 \pi}{12} \frac{3 \pi}{4} \frac{7 \pi}{12} \frac{5 \pi}{12} \frac{\pi}{4} \frac{\pi}{12} \cdot - \frac{\pi}{12} \cdot - \frac{\pi}{4} \cdot - \frac{5 \pi}{12} \cdot - \frac{7 \pi}{12} \cdot - \frac{11 \pi}{12} \left(- \frac{3 \pi}{4}\right)$$

         12
148225*pi  
-----------
12230590464

$$\frac{148225 \pi^{12}}{12230590464}$$

148225*pi^12/12230590464

Numerical answer [src]

x1 = 10.2101761241668

x2 = 50.0036830696375

x3 = -79.8488132787406

x4 = -67.8060414399797

x5 = 96.0803753222878

x6 = 68.329640215578

x7 = -91.8915851175014

x8 = 3.92699081698724

x9 = 78.2780169519457

x10 = -3.92699081698724

x11 = 80.3724120543389

x12 = 74.0892267471593

x13 = -87.7027949127151

x14 = -11.7809724509617

x15 = -9.68657734856853

x16 = 12.30457122656

x17 = -73.565627971561

x18 = -15.9697626557481

x19 = 69.9004365423729

x20 = 98.174770424681

x21 = -25.9181393921158

x22 = -7.59218224617533

x23 = 8.11578102177363

x24 = -43.720497762458

x25 = -1.83259571459405

x26 = 86.1319985859202

x27 = -33.7721210260903

x28 = -71.9948316447661

x29 = 14.3989663289532

x30 = -57.857664703612

x31 = -18.0641577581413

x32 = -96.0803753222878

x33 = -75.6600230739542

x34 = -81.9432083811338

x35 = -51.5744793964324

x36 = -69.9004365423729

x37 = 6.02138591938044

x38 = 2.35619449019234

x39 = -19.6349540849362

x40 = -45.8148928648512

x41 = 24.3473430653209

x42 = -97.6511716490827

x43 = 88.2263936883134

x44 = -85.6083998103219

x45 = -6.02138591938044

x46 = -77.7544181763474

x47 = 71.9948316447661

x48 = 90.3207887907066

x49 = 30.1069295969022

x50 = -35.8665161284835

x51 = 40.0553063332699

x52 = 58.3812634792103

x53 = 44.2440965380563

x54 = 20.1585528605345

x55 = -37.9609112308767

x56 = 59.9520598060052

x57 = 56.2868683768171

x58 = -62.0464549083984

x59 = -59.9520598060052

x60 = 84.037603483527

x61 = -63.6172512351933

x62 = 54.1924732744239

x63 = 37.9609112308767

x64 = -99.7455667514759

x65 = 42.1497014356631

x66 = 46.3384916404494

x67 = -13.8753675533549

x68 = -31.6777259236971

x69 = -41.6261026600648

x70 = 64.1408500107916

x71 = -93.9859802198946

x72 = 47.9092879672443

x73 = 18.0641577581413

x74 = -55.7632696012188

x75 = 52.0980781720307

x76 = -47.9092879672443

x77 = -53.6688744988256

x78 = 100.269165527074

x79 = 93.9859802198946

x80 = -50.0036830696375

x81 = 62.0464549083984

x82 = 15.9697626557481

x83 = 32.2013246992954

x84 = -29.5833308213039

x85 = -89.7971900151083

x86 = 66.2352451131848

x87 = 36.3901149040818

x88 = -84.037603483527

x89 = 22.2529479629277

x90 = -23.8237442897226

x91 = 76.1836218495525

x92 = 28.012534494509

x93 = -21.7293491873294

x94 = 25.9181393921158

x95 = -40.0553063332699

x96 = 34.2957198016886

x97 = 81.9432083811338

x98 = -28.012534494509

x99 = -65.7116463375865

x100 = 91.8915851175014

x100 = 91.8915851175014

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Identical expressions

Similar expressions

cos^2(2x)+cos^2(4x)=1+ctg(6x) equation

Numerical solution:

The solution