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Equation:
Equation cos(x)=-2
Equation 17x-8=20x+7
Equation 9*(x-5)=-x
Equation x^2+2x-3=0
Express {x} in terms of y where:
7*x+19*y=12
2*x+2*y=-6
10*x-2*y=0
12*x-13*y=-14
Identical expressions
sinx+cosx/sinx=2cotx
sinus of x plus co sinus of e of x divide by sinus of x equally 2 cotangent of x
sinx+cosx divide by sinx=2cotx
Similar expressions
(tan(x)-2*cot(x))+1=0
sinx-cosx/sinx=2cotx
2*sin(x)^2*cot(x)+sin(4*x-pi/2)+1=0
sqrt(2*cot(x))-1=0
3*tan(x)+2*cot(x)+5=0

sinx+cosx/sinx=2cotx equation

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The solution

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         cos(x)           
sin(x) + ------ = 2*cot(x)
         sin(x)

$$\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} = 2 \cot{\left(x \right)}$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Sum and product of roots [src]

sum

                               /      __________________________________________________________________________________________________________________________________________________\          /      __________________________________________________________________________________________________________________________________________________\                                                                                                                      
                               |     /                       ___________            ___________        ___________    ____________              ____________               ____________ |          |     /                      ___________             ___________        ___________    ____________               ____________              ____________ |                                                                                                                      
      /       ___     \        |    /        ___     ____   /       ___      ___   /       ___        /       ___    /        ___        ___   /        ___        ____   /        ___  |          |    /        ___     ___   /       ___      ____   /       ___        /       ___    /        ___        ____   /        ___        ___   /        ___  |       /       ___     \                                                                                              
      |     \/ 2      |        |   /   3   \/ 5    \/ 10 *\/  1 - \/ 5     \/ 2 *\/  1 - \/ 5     I*\/  1 - \/ 5  *\/  -1 + \/ 5     I*\/ 2 *\/  -1 + \/ 5     I*\/ 10 *\/  -1 + \/ 5   |          |   /   3   \/ 5    \/ 2 *\/  1 - \/ 5     \/ 10 *\/  1 - \/ 5     I*\/  1 - \/ 5  *\/  -1 + \/ 5     I*\/ 10 *\/  -1 + \/ 5     I*\/ 2 *\/  -1 + \/ 5   |       |     \/ 2      |             /               2                \             /               2                \
- atan|---------------| - I*log|  /    - - ----- - --------------------- + -------------------- - -------------------------------- - ----------------------- + ------------------------ | + - I*log|  /    - - ----- - -------------------- + --------------------- - -------------------------------- - ------------------------ + ----------------------- | + atan|---------------| + pi + I*log|--------------------------------| + pi + I*log|--------------------------------|
      |   ____________|        \\/     2     2               4                      4                            2                              4                         4             /          \\/     2     2              4                       4                            2                              4                          4            /       |   ____________|             |                     ___________|             |                     ___________|
      |  /        ___ |                                                                                                                                                                                                                                                                                                                                             |  /        ___ |             |      ___     ___   /       ___ |             |      ___     ___   /       ___ |
      \\/  -1 + \/ 5  /                                                                                                                                                                                                                                                                                                                                             \\/  -1 + \/ 5  /             \1 + \/ 5  + \/ 2 *\/  1 + \/ 5  /             \1 + \/ 5  - \/ 2 *\/  1 + \/ 5  /

$$\left(\left(\left(- \operatorname{atan}{\left(\frac{\sqrt{2}}{\sqrt{-1 + \sqrt{5}}} \right)} - i \log{\left(\sqrt{- \frac{\sqrt{5}}{2} - \frac{i \sqrt{-1 + \sqrt{5}} \sqrt{1 - \sqrt{5}}}{2} + \frac{3}{2} - \frac{\sqrt{10} \sqrt{1 - \sqrt{5}}}{4} - \frac{\sqrt{2} i \sqrt{-1 + \sqrt{5}}}{4} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{4} + \frac{\sqrt{10} i \sqrt{-1 + \sqrt{5}}}{4}} \right)}\right) + \left(- i \log{\left(\sqrt{- \frac{\sqrt{5}}{2} - \frac{i \sqrt{-1 + \sqrt{5}} \sqrt{1 - \sqrt{5}}}{2} + \frac{3}{2} - \frac{\sqrt{10} i \sqrt{-1 + \sqrt{5}}}{4} - \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{4} + \frac{\sqrt{2} i \sqrt{-1 + \sqrt{5}}}{4} + \frac{\sqrt{10} \sqrt{1 - \sqrt{5}}}{4}} \right)} + \operatorname{atan}{\left(\frac{\sqrt{2}}{\sqrt{-1 + \sqrt{5}}} \right)}\right)\right) + \left(\pi + i \log{\left(\frac{2}{1 + \sqrt{5} + \sqrt{2} \sqrt{1 + \sqrt{5}}} \right)}\right)\right) + \left(\pi + i \log{\left(\frac{2}{- \sqrt{2} \sqrt{1 + \sqrt{5}} + 1 + \sqrt{5}} \right)}\right)$$

                                                                                                /      __________________________________________________________________________________________________________________________________________________\        /      __________________________________________________________________________________________________________________________________________________\
                                                                                                |     /                      ___________             ___________        ___________    ____________               ____________              ____________ |        |     /                       ___________            ___________        ___________    ____________              ____________               ____________ |
                                                                                                |    /        ___     ___   /       ___      ____   /       ___        /       ___    /        ___        ____   /        ___        ___   /        ___  |        |    /        ___     ____   /       ___      ___   /       ___        /       ___    /        ___        ___   /        ___        ____   /        ___  |
            /               2                \        /               2                \        |   /   3   \/ 5    \/ 2 *\/  1 - \/ 5     \/ 10 *\/  1 - \/ 5     I*\/  1 - \/ 5  *\/  -1 + \/ 5     I*\/ 10 *\/  -1 + \/ 5     I*\/ 2 *\/  -1 + \/ 5   |        |   /   3   \/ 5    \/ 10 *\/  1 - \/ 5     \/ 2 *\/  1 - \/ 5     I*\/  1 - \/ 5  *\/  -1 + \/ 5     I*\/ 2 *\/  -1 + \/ 5     I*\/ 10 *\/  -1 + \/ 5   |
2*pi + I*log|--------------------------------| + I*log|--------------------------------| - I*log|  /    - - ----- - -------------------- + --------------------- - -------------------------------- - ------------------------ + ----------------------- | - I*log|  /    - - ----- - --------------------- + -------------------- - -------------------------------- - ----------------------- + ------------------------ |
            |                     ___________|        |                     ___________|        \\/     2     2              4                       4                            2                              4                          4            /        \\/     2     2               4                      4                            2                              4                         4             /
            |      ___     ___   /       ___ |        |      ___     ___   /       ___ |                                                                                                                                                                                                                                                                                                                                    
            \1 + \/ 5  + \/ 2 *\/  1 + \/ 5  /        \1 + \/ 5  - \/ 2 *\/  1 + \/ 5  /

$$- i \log{\left(\sqrt{- \frac{\sqrt{5}}{2} - \frac{i \sqrt{-1 + \sqrt{5}} \sqrt{1 - \sqrt{5}}}{2} + \frac{3}{2} - \frac{\sqrt{10} i \sqrt{-1 + \sqrt{5}}}{4} - \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{4} + \frac{\sqrt{2} i \sqrt{-1 + \sqrt{5}}}{4} + \frac{\sqrt{10} \sqrt{1 - \sqrt{5}}}{4}} \right)} - i \log{\left(\sqrt{- \frac{\sqrt{5}}{2} - \frac{i \sqrt{-1 + \sqrt{5}} \sqrt{1 - \sqrt{5}}}{2} + \frac{3}{2} - \frac{\sqrt{10} \sqrt{1 - \sqrt{5}}}{4} - \frac{\sqrt{2} i \sqrt{-1 + \sqrt{5}}}{4} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{4} + \frac{\sqrt{10} i \sqrt{-1 + \sqrt{5}}}{4}} \right)} + 2 \pi + i \log{\left(\frac{2}{1 + \sqrt{5} + \sqrt{2} \sqrt{1 + \sqrt{5}}} \right)} + i \log{\left(\frac{2}{- \sqrt{2} \sqrt{1 + \sqrt{5}} + 1 + \sqrt{5}} \right)}$$

product

/                               /      __________________________________________________________________________________________________________________________________________________\\ /       /      __________________________________________________________________________________________________________________________________________________\                        \                                                                                              
|                               |     /                       ___________            ___________        ___________    ____________              ____________               ____________ || |       |     /                      ___________             ___________        ___________    ____________               ____________              ____________ |                        |                                                                                              
|      /       ___     \        |    /        ___     ____   /       ___      ___   /       ___        /       ___    /        ___        ___   /        ___        ____   /        ___  || |       |    /        ___     ___   /       ___      ____   /       ___        /       ___    /        ___        ____   /        ___        ___   /        ___  |       /       ___     \|                                                                                              
|      |     \/ 2      |        |   /   3   \/ 5    \/ 10 *\/  1 - \/ 5     \/ 2 *\/  1 - \/ 5     I*\/  1 - \/ 5  *\/  -1 + \/ 5     I*\/ 2 *\/  -1 + \/ 5     I*\/ 10 *\/  -1 + \/ 5   || |       |   /   3   \/ 5    \/ 2 *\/  1 - \/ 5     \/ 10 *\/  1 - \/ 5     I*\/  1 - \/ 5  *\/  -1 + \/ 5     I*\/ 10 *\/  -1 + \/ 5     I*\/ 2 *\/  -1 + \/ 5   |       |     \/ 2      || /          /               2                \\ /          /               2                \\
|- atan|---------------| - I*log|  /    - - ----- - --------------------- + -------------------- - -------------------------------- - ----------------------- + ------------------------ ||*|- I*log|  /    - - ----- - -------------------- + --------------------- - -------------------------------- - ------------------------ + ----------------------- | + atan|---------------||*|pi + I*log|--------------------------------||*|pi + I*log|--------------------------------||
|      |   ____________|        \\/     2     2               4                      4                            2                              4                         4             /| |       \\/     2     2              4                       4                            2                              4                          4            /       |   ____________|| |          |                     ___________|| |          |                     ___________||
|      |  /        ___ |                                                                                                                                                                  | |                                                                                                                                                                        |  /        ___ || |          |      ___     ___   /       ___ || |          |      ___     ___   /       ___ ||
\      \\/  -1 + \/ 5  /                                                                                                                                                                  / \                                                                                                                                                                        \\/  -1 + \/ 5  // \          \1 + \/ 5  + \/ 2 *\/  1 + \/ 5  // \          \1 + \/ 5  - \/ 2 *\/  1 + \/ 5  //

$$\left(- i \log{\left(\sqrt{- \frac{\sqrt{5}}{2} - \frac{i \sqrt{-1 + \sqrt{5}} \sqrt{1 - \sqrt{5}}}{2} + \frac{3}{2} - \frac{\sqrt{10} i \sqrt{-1 + \sqrt{5}}}{4} - \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{4} + \frac{\sqrt{2} i \sqrt{-1 + \sqrt{5}}}{4} + \frac{\sqrt{10} \sqrt{1 - \sqrt{5}}}{4}} \right)} + \operatorname{atan}{\left(\frac{\sqrt{2}}{\sqrt{-1 + \sqrt{5}}} \right)}\right) \left(- \operatorname{atan}{\left(\frac{\sqrt{2}}{\sqrt{-1 + \sqrt{5}}} \right)} - i \log{\left(\sqrt{- \frac{\sqrt{5}}{2} - \frac{i \sqrt{-1 + \sqrt{5}} \sqrt{1 - \sqrt{5}}}{2} + \frac{3}{2} - \frac{\sqrt{10} \sqrt{1 - \sqrt{5}}}{4} - \frac{\sqrt{2} i \sqrt{-1 + \sqrt{5}}}{4} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{4} + \frac{\sqrt{10} i \sqrt{-1 + \sqrt{5}}}{4}} \right)}\right) \left(\pi + i \log{\left(\frac{2}{1 + \sqrt{5} + \sqrt{2} \sqrt{1 + \sqrt{5}}} \right)}\right) \left(\pi + i \log{\left(\frac{2}{- \sqrt{2} \sqrt{1 + \sqrt{5}} + 1 + \sqrt{5}} \right)}\right)$$

                                                                                              /                               /    _______________________________________________________________________________________________________\\ /     /    _______________________________________________________________________________________________________\                        \
                                                                                              |                               |   /               ___________            ___________              ____________               ____________ || |     |   /              ___________             ___________               ____________              ____________ |                        |
                                                                                              |      /       ___     \        |  /        ____   /       ___      ___   /       ___        ___   /        ___        ____   /        ___  || |     |  /        ___   /       ___      ____   /       ___        ____   /        ___        ___   /        ___  |       /       ___     \|
/          /               2                \\ /          /               2                \\ |      |     \/ 2      |        |\/   4 + \/ 10 *\/  1 - \/ 5   - \/ 2 *\/  1 - \/ 5   + I*\/ 2 *\/  -1 + \/ 5   - I*\/ 10 *\/  -1 + \/ 5   || |     |\/   4 + \/ 2 *\/  1 - \/ 5   - \/ 10 *\/  1 - \/ 5   + I*\/ 10 *\/  -1 + \/ 5   - I*\/ 2 *\/  -1 + \/ 5   |       |     \/ 2      ||
|pi + I*log|--------------------------------||*|pi + I*log|--------------------------------||*|- atan|---------------| + I*log|-----------------------------------------------------------------------------------------------------------||*|I*log|-----------------------------------------------------------------------------------------------------------| + atan|---------------||
|          |                     ___________|| |          |                     ___________|| |      |   ____________|        \                                                     2                                                     /| |     \                                                     2                                                     /       |   ____________||
|          |      ___     ___   /       ___ || |          |      ___     ___   /       ___ || |      |  /        ___ |                                                                                                                     | |                                                                                                                         |  /        ___ ||
\          \1 + \/ 5  + \/ 2 *\/  1 + \/ 5  // \          \1 + \/ 5  - \/ 2 *\/  1 + \/ 5  // \      \\/  -1 + \/ 5  /                                                                                                                     / \                                                                                                                         \\/  -1 + \/ 5  //

$$\left(\pi + i \log{\left(\frac{2}{1 + \sqrt{5} + \sqrt{2} \sqrt{1 + \sqrt{5}}} \right)}\right) \left(\pi + i \log{\left(\frac{2}{- \sqrt{2} \sqrt{1 + \sqrt{5}} + 1 + \sqrt{5}} \right)}\right) \left(i \log{\left(\frac{\sqrt{4 - \sqrt{10} \sqrt{1 - \sqrt{5}} - \sqrt{2} i \sqrt{-1 + \sqrt{5}} + \sqrt{2} \sqrt{1 - \sqrt{5}} + \sqrt{10} i \sqrt{-1 + \sqrt{5}}}}{2} \right)} + \operatorname{atan}{\left(\frac{\sqrt{2}}{\sqrt{-1 + \sqrt{5}}} \right)}\right) \left(- \operatorname{atan}{\left(\frac{\sqrt{2}}{\sqrt{-1 + \sqrt{5}}} \right)} + i \log{\left(\frac{\sqrt{4 - \sqrt{10} i \sqrt{-1 + \sqrt{5}} - \sqrt{2} \sqrt{1 - \sqrt{5}} + \sqrt{2} i \sqrt{-1 + \sqrt{5}} + \sqrt{10} \sqrt{1 - \sqrt{5}}}}{2} \right)}\right)$$

(pi + i*log(2/(1 + sqrt(5) + sqrt(2)*sqrt(1 + sqrt(5)))))*(pi + i*log(2/(1 + sqrt(5) - sqrt(2)*sqrt(1 + sqrt(5)))))*(-atan(sqrt(2)/sqrt(-1 + sqrt(5))) + i*log(sqrt(4 + sqrt(10)*sqrt(1 - sqrt(5)) - sqrt(2)*sqrt(1 - sqrt(5)) + i*sqrt(2)*sqrt(-1 + sqrt(5)) - i*sqrt(10)*sqrt(-1 + sqrt(5)))/2))*(i*log(sqrt(4 + sqrt(2)*sqrt(1 - sqrt(5)) - sqrt(10)*sqrt(1 - sqrt(5)) + i*sqrt(10)*sqrt(-1 + sqrt(5)) - i*sqrt(2)*sqrt(-1 + sqrt(5)))/2) + atan(sqrt(2)/sqrt(-1 + sqrt(5))))

Rapid solution [src]

                                    /      __________________________________________________________________________________________________________________________________________________\
                                    |     /                       ___________            ___________        ___________    ____________              ____________               ____________ |
           /       ___     \        |    /        ___     ____   /       ___      ___   /       ___        /       ___    /        ___        ___   /        ___        ____   /        ___  |
           |     \/ 2      |        |   /   3   \/ 5    \/ 10 *\/  1 - \/ 5     \/ 2 *\/  1 - \/ 5     I*\/  1 - \/ 5  *\/  -1 + \/ 5     I*\/ 2 *\/  -1 + \/ 5     I*\/ 10 *\/  -1 + \/ 5   |
x1 = - atan|---------------| - I*log|  /    - - ----- - --------------------- + -------------------- - -------------------------------- - ----------------------- + ------------------------ |
           |   ____________|        \\/     2     2               4                      4                            2                              4                         4             /
           |  /        ___ |                                                                                                                                                                  
           \\/  -1 + \/ 5  /

$$x_{1} = - \operatorname{atan}{\left(\frac{\sqrt{2}}{\sqrt{-1 + \sqrt{5}}} \right)} - i \log{\left(\sqrt{- \frac{\sqrt{5}}{2} - \frac{i \sqrt{-1 + \sqrt{5}} \sqrt{1 - \sqrt{5}}}{2} + \frac{3}{2} - \frac{\sqrt{10} \sqrt{1 - \sqrt{5}}}{4} - \frac{\sqrt{2} i \sqrt{-1 + \sqrt{5}}}{4} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{4} + \frac{\sqrt{10} i \sqrt{-1 + \sqrt{5}}}{4}} \right)}$$

            /      __________________________________________________________________________________________________________________________________________________\                        
            |     /                      ___________             ___________        ___________    ____________               ____________              ____________ |                        
            |    /        ___     ___   /       ___      ____   /       ___        /       ___    /        ___        ____   /        ___        ___   /        ___  |       /       ___     \
            |   /   3   \/ 5    \/ 2 *\/  1 - \/ 5     \/ 10 *\/  1 - \/ 5     I*\/  1 - \/ 5  *\/  -1 + \/ 5     I*\/ 10 *\/  -1 + \/ 5     I*\/ 2 *\/  -1 + \/ 5   |       |     \/ 2      |
x2 = - I*log|  /    - - ----- - -------------------- + --------------------- - -------------------------------- - ------------------------ + ----------------------- | + atan|---------------|
            \\/     2     2              4                       4                            2                              4                          4            /       |   ____________|
                                                                                                                                                                             |  /        ___ |
                                                                                                                                                                             \\/  -1 + \/ 5  /

$$x_{2} = - i \log{\left(\sqrt{- \frac{\sqrt{5}}{2} - \frac{i \sqrt{-1 + \sqrt{5}} \sqrt{1 - \sqrt{5}}}{2} + \frac{3}{2} - \frac{\sqrt{10} i \sqrt{-1 + \sqrt{5}}}{4} - \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{4} + \frac{\sqrt{2} i \sqrt{-1 + \sqrt{5}}}{4} + \frac{\sqrt{10} \sqrt{1 - \sqrt{5}}}{4}} \right)} + \operatorname{atan}{\left(\frac{\sqrt{2}}{\sqrt{-1 + \sqrt{5}}} \right)}$$

               /               2                \
x3 = pi + I*log|--------------------------------|
               |                     ___________|
               |      ___     ___   /       ___ |
               \1 + \/ 5  + \/ 2 *\/  1 + \/ 5  /

$$x_{3} = \pi + i \log{\left(\frac{2}{1 + \sqrt{5} + \sqrt{2} \sqrt{1 + \sqrt{5}}} \right)}$$

               /               2                \
x4 = pi + I*log|--------------------------------|
               |                     ___________|
               |      ___     ___   /       ___ |
               \1 + \/ 5  - \/ 2 *\/  1 + \/ 5  /

$$x_{4} = \pi + i \log{\left(\frac{2}{- \sqrt{2} \sqrt{1 + \sqrt{5}} + 1 + \sqrt{5}} \right)}$$

x4 = pi + i*log(2/(-sqrt(2)*sqrt(1 + sqrt(5)) + 1 + sqrt(5)))

Numerical answer [src]

x1 = -13.4709275086616

x2 = -87.0600374062118

x3 = -49.3609255631343

x4 = -19.7541128158411

x5 = -43.0777402559547

x6 = -32.3204834302003

x7 = 63.7364099660982

x8 = -99.626408020571

x9 = 13.4709275086616

x10 = 43.0777402559547

x11 = -82.585965887637

x12 = -7.18774220148197

x13 = 0.904556894302381

x14 = 95.1523365019962

x15 = -61.9272961774935

x16 = -26.0372981230207

x17 = 57.4532246589187

x18 = 76.3027805804574

x19 = 74.4936667918527

x20 = -74.4936667918527

x21 = -5.37862841287721

x22 = -70.0195952732778

x23 = -57.4532246589187

x24 = 80.7768520990322

x25 = -93.3432227133914

x26 = 61.9272961774935

x27 = 70.0195952732778

x28 = -95.1523365019962

x29 = 30.5113696415956

x30 = 93.3432227133914

x31 = 38.6036687373799

x32 = 19.7541128158411

x33 = 17.9449990272364

x34 = -63.7364099660982

x35 = -36.7945549487751

x36 = -55.6441108703139

x37 = 36.7945549487751

x38 = 68.2104814846731

x39 = -51.1700393517391

x40 = -0.904556894302381

x41 = 26.0372981230207

x42 = -38.6036687373799

x43 = 55.6441108703139

x44 = -80.7768520990322

x45 = 99.626408020571

x46 = -76.3027805804574

x47 = 11.6618137200568

x48 = -11.6618137200568

x49 = -17.9449990272364

x50 = 7.18774220148197

x51 = 24.228184334416

x52 = 32.3204834302003

x53 = -44.8868540445595

x54 = 5.37862841287721

x55 = 44.8868540445595

x56 = 88.8691511948166

x57 = -24.228184334416

x58 = -68.2104814846731

x59 = 82.585965887637

x60 = -30.5113696415956

x61 = 49.3609255631343

x62 = -88.8691511948166

x63 = 87.0600374062118

x64 = 51.1700393517391

x64 = 51.1700393517391

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Identical expressions

Similar expressions

sinx+cosx/sinx=2cotx equation

Numerical solution:

The solution