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Equation:
Equation x^2-8*x+17=0
Equation 9x-26=30-5x
Equation x+19=12
Equation 2x+2=-3
Express {x} in terms of y where:
2*x+13*y=19
17*x-20*y=6
5*x-13*y=17
11*x-20*y=-10
Identical expressions
eight *cos(2x)*cos(4x)*cos(8x)= one
8 multiply by co sinus of e of (2x) multiply by co sinus of e of (4x) multiply by co sinus of e of (8x) equally 1
eight multiply by co sinus of e of (2x) multiply by co sinus of e of (4x) multiply by co sinus of e of (8x) equally one
8cos(2x)cos(4x)cos(8x)=1
8cos2xcos4xcos8x=1

8cos(2x)cos(4x)*cos(8x)=1 equation

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

The solution

You have entered [src]

8*cos(2*x)*cos(4*x)*cos(8*x) = 1

$$8 \cos{\left(2 x \right)} \cos{\left(4 x \right)} \cos{\left(8 x \right)} = 1$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

     -5*pi
x1 = -----
       6

$$x_{1} = - \frac{5 \pi}{6}$$

     -2*pi
x2 = -----
       7

$$x_{2} = - \frac{2 \pi}{7}$$

     -5*pi
x3 = -----
       18

$$x_{3} = - \frac{5 \pi}{18}$$

     -pi 
x4 = ----
      6

$$x_{4} = - \frac{\pi}{6}$$

     -pi 
x5 = ----
      7

$$x_{5} = - \frac{\pi}{7}$$

     -pi 
x6 = ----
      18

$$x_{6} = - \frac{\pi}{18}$$

     pi
x7 = --
     18

$$x_{7} = \frac{\pi}{18}$$

     pi
x8 = --
     7

$$x_{8} = \frac{\pi}{7}$$

     pi
x9 = --
     6

$$x_{9} = \frac{\pi}{6}$$

      5*pi
x10 = ----
       18

$$x_{10} = \frac{5 \pi}{18}$$

      2*pi
x11 = ----
       7

$$x_{11} = \frac{2 \pi}{7}$$

      5*pi
x12 = ----
       7

$$x_{12} = \frac{5 \pi}{7}$$

      13*pi
x13 = -----
        18

$$x_{13} = \frac{13 \pi}{18}$$

      5*pi
x14 = ----
       6

$$x_{14} = \frac{5 \pi}{6}$$

      6*pi
x15 = ----
       7

$$x_{15} = \frac{6 \pi}{7}$$

      17*pi
x16 = -----
        18

$$x_{16} = \frac{17 \pi}{18}$$

            / 18____\
x17 = -I*log\-\/ -1 /

$$x_{17} = - i \log{\left(- \sqrt[18]{-1} \right)}$$

            / 7 ____\
x18 = -I*log\-\/ -1 /

$$x_{18} = - i \log{\left(- \sqrt[7]{-1} \right)}$$

                                                   /   /pi\\
                 /    _____________________\       |cos|--||
                 |   /    2/pi\      2/pi\ |       |   \14/|
x19 = -pi - I*log|  /  cos |--| + sin |--| | + atan|-------|
                 \\/       \14/       \14/ /       |   /pi\|
                                                   |sin|--||
                                                   \   \14//

$$x_{19} = - \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)}$$

               /   /pi\\                                   
               |cos|--||        /    _____________________\
               |   \14/|        |   /    2/pi\      2/pi\ |
x20 = pi - atan|-------| - I*log|  /  cos |--| + sin |--| |
               |   /pi\|        \\/       \14/       \14/ /
               |sin|--||                                   
               \   \14//

$$x_{20} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \pi$$

            /   /pi\\                                   
            |cos|--||        /    _____________________\
            |   \14/|        |   /    2/pi\      2/pi\ |
x21 = - atan|-------| - I*log|  /  cos |--| + sin |--| |
            |   /pi\|        \\/       \14/       \14/ /
            |sin|--||                                   
            \   \14//

$$x_{21} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)}$$

                                               /   /pi\\
             /    _____________________\       |cos|--||
             |   /    2/pi\      2/pi\ |       |   \14/|
x22 = - I*log|  /  cos |--| + sin |--| | + atan|-------|
             \\/       \14/       \14/ /       |   /pi\|
                                               |sin|--||
                                               \   \14//

$$x_{22} = - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)}$$

                                                   /   /pi\\
                 /    _____________________\       |cos|--||
                 |   /    2/pi\      2/pi\ |       |   \9 /|
x23 = -pi - I*log|  /  cos |--| + sin |--| | + atan|-------|
                 \\/       \9 /       \9 / /       |   /pi\|
                                                   |sin|--||
                                                   \   \9 //

$$x_{23} = - \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{9} \right)} + \cos^{2}{\left(\frac{\pi}{9} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{9} \right)}}{\sin{\left(\frac{\pi}{9} \right)}} \right)}$$

               /   /pi\\                                   
               |cos|--||        /    _____________________\
               |   \9 /|        |   /    2/pi\      2/pi\ |
x24 = pi - atan|-------| - I*log|  /  cos |--| + sin |--| |
               |   /pi\|        \\/       \9 /       \9 / /
               |sin|--||                                   
               \   \9 //

$$x_{24} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{9} \right)}}{\sin{\left(\frac{\pi}{9} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{9} \right)} + \cos^{2}{\left(\frac{\pi}{9} \right)}} \right)} + \pi$$

            /   /pi\\                                   
            |cos|--||        /    _____________________\
            |   \9 /|        |   /    2/pi\      2/pi\ |
x25 = - atan|-------| - I*log|  /  cos |--| + sin |--| |
            |   /pi\|        \\/       \9 /       \9 / /
            |sin|--||                                   
            \   \9 //

$$x_{25} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{9} \right)}}{\sin{\left(\frac{\pi}{9} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{9} \right)} + \cos^{2}{\left(\frac{\pi}{9} \right)}} \right)}$$

                                               /   /pi\\
             /    _____________________\       |cos|--||
             |   /    2/pi\      2/pi\ |       |   \9 /|
x26 = - I*log|  /  cos |--| + sin |--| | + atan|-------|
             \\/       \9 /       \9 / /       |   /pi\|
                                               |sin|--||
                                               \   \9 //

$$x_{26} = - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{9} \right)} + \cos^{2}{\left(\frac{\pi}{9} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{9} \right)}}{\sin{\left(\frac{\pi}{9} \right)}} \right)}$$

                                                       /   /3*pi\\
                 /    _________________________\       |cos|----||
                 |   /    2/3*pi\      2/3*pi\ |       |   \ 14 /|
x27 = -pi - I*log|  /  cos |----| + sin |----| | + atan|---------|
                 \\/       \ 14 /       \ 14 / /       |   /3*pi\|
                                                       |sin|----||
                                                       \   \ 14 //

$$x_{27} = - \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{14} \right)} + \cos^{2}{\left(\frac{3 \pi}{14} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{3 \pi}{14} \right)}}{\sin{\left(\frac{3 \pi}{14} \right)}} \right)}$$

                                                       /   /2*pi\\
                 /    _________________________\       |cos|----||
                 |   /    2/2*pi\      2/2*pi\ |       |   \ 9  /|
x28 = -pi - I*log|  /  cos |----| + sin |----| | + atan|---------|
                 \\/       \ 9  /       \ 9  / /       |   /2*pi\|
                                                       |sin|----||
                                                       \   \ 9  //

$$x_{28} = - \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{2 \pi}{9} \right)} + \cos^{2}{\left(\frac{2 \pi}{9} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{2 \pi}{9} \right)}}{\sin{\left(\frac{2 \pi}{9} \right)}} \right)}$$

x28 = -pi - i*log(sqrt(sin(2*pi/9)^2 + cos(2*pi/9)^2)) + atan(cos(2*pi/9)/sin(2*pi/9))

Numerical answer [src]

x1 = 90.2335223281068

x2 = 60.2138591938044

x3 = 88.1391272257137

x4 = -54.3046730120521

x5 = -93.7241808320955

x6 = -89.7597901025655

x7 = -35.7792496658838

x8 = -17.9768912955416

x9 = 9.94837673636768

x10 = 338.768407812099

x11 = -19.7471538225644

x12 = 98.2620368872808

x13 = 40.317105721069

x14 = 68.2423737529783

x15 = -39.9680398706701

x16 = -26.0054058547155

x17 = 194.255145746969

x18 = 92.0037848551297

x19 = 83.0278058448731

x20 = 41.7133691226645

x21 = 47.9965544298441

x22 = -64.0535835481919

x23 = -41.738302397693

x24 = -5.75958653158129

x25 = 28.0998009571087

x26 = 56.025068989018

x27 = 73.1292956585624

x28 = -92.0037848551297

x29 = -96.0429754097451

x30 = 548.906049752217

x31 = 8.20304748437335

x32 = -85.6956662729216

x33 = -31.9395253114962

x34 = -49.7418836818384

x35 = -63.7294509728215

x36 = 70.0126362800011

x37 = -13.0899693899575

x38 = 39.9431065956417

x39 = -87.7900613753148

x40 = -79.7615468161409

x41 = 22.165681500328

x42 = -37.873644768277

x43 = 26.0054058547155

x44 = -43.8077642250577

x45 = 16.2315620435473

x46 = -4.01425727958696

x47 = -21.8166156499291

x48 = -13.7881010907552

x49 = -27.7507351067098

x50 = 78.0162175641465

x51 = -52.1853446346305

x52 = -85.7205995479501

x53 = -59.8647933434055

x54 = 50.0909495322373

x55 = 94.0732466824944

x56 = -55.3269372882203

x57 = 46.2512251778497

x58 = -69.9877030049726

x59 = 24.2600766027212

x60 = 76.2708883121522

x61 = -116.687727133335

x62 = -65.7989128001862

x63 = -45.7774929523084

x64 = -81.8559419185341

x65 = -71.733032256967

x66 = -74.0518268346165

x67 = 85.3466004225227

x68 = -25.6563400043166

x69 = 17.9768912955416

x70 = -57.7703982410123

x71 = 4.01425727958696

x72 = 2.24399475256414

x73 = 6.10865238198015

x74 = 0.174532925199433

x75 = 33.6599212884621

x76 = 54.3046730120521

x77 = -34.0339204138894

x78 = 100.007366139275

x79 = 30.5432619099008

x80 = 80.8087443673375

x81 = 82.2050077689329

x82 = -30.1941960595019

x83 = 44.1568300754565

x84 = -78.0162175641465

x85 = 19.3731546971371

x86 = 1408.33110670925

x87 = 72.0820981073658

x88 = -67.768641527437

x89 = 13.0899693899575

x90 = -15.8824961931484

x91 = 52.5344104850293

x92 = 135.961148730358

x93 = -47.9965544298441

x94 = 66.1479786505851

x95 = -100.007366139275

x96 = 38.2227106186758

x96 = 38.2227106186758

Other calculators

How to use it?

Identical expressions

8*cos(2x)*cos(4x)*cos(8x)=1 equation

Numerical solution:

The solution

8cos(2x)cos(4x)*cos(8x)=1 equation