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Equation:
Equation 2(x+4)(x+2)=x^2+2x
Equation tan(x)=0.8
Equation (arcctg(x)-arctg(x))x^2-2x+arcctg(x)-arctg(x)
Equation sinx+|cosx|=sin4x+cos2x
Express {x} in terms of y where:
(x^2+y^2-1)^3+x^2*y^3=0
-1*x-19*y=-10
5*x+5*y=20
4*x-16*y=6
Identical expressions
four /(one -cos^ two *x)-(five /sinx)= six
4 divide by (1 minus co sinus of e of squared multiply by x) minus (5 divide by sinus of x) equally 6
four divide by (one minus co sinus of e of to the power of two multiply by x) minus (five divide by sinus of x) equally six
4/(1-cos2*x)-(5/sinx)=6
4/1-cos2*x-5/sinx=6
4/(1-cos²*x)-(5/sinx)=6
4/(1-cos to the power of 2*x)-(5/sinx)=6
4/(1-cos^2x)-(5/sinx)=6
4/(1-cos2x)-(5/sinx)=6
4/1-cos2x-5/sinx=6
4/1-cos^2x-5/sinx=6
4 divide by (1-cos^2*x)-(5 divide by sinx)=6
Similar expressions
4/(1-cos^2*x)+(5/sinx)=6
4/(1+cos^2*x)-(5/sinx)=6

4/(1-cos^2*x)-(5/sinx)=6 equation

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The solution

You have entered [src]

     4          5       
----------- - ------ = 6
       2      sin(x)    
1 - cos (x)

$$- \frac{5}{\sin{\left(x \right)}} + \frac{4}{- \cos^{2}{\left(x \right)} + 1} = 6$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Sum and product of roots [src]

sum

                  /    /        ___\\         /    /        ___\\         /    /        ___\\         /    /        ___\\
pi   5*pi         |    |3   I*\/ 7 ||         |    |3   I*\/ 7 ||         |    |3   I*\/ 7 ||         |    |3   I*\/ 7 ||
-- + ---- + - 2*re|atan|- - -------|| - 2*I*im|atan|- - -------|| + - 2*re|atan|- + -------|| - 2*I*im|atan|- + -------||
6     6           \    \4      4   //         \    \4      4   //         \    \4      4   //         \    \4      4   //

$$\left(\frac{\pi}{6}\right) + \left(\frac{5 \pi}{6}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{4} - \frac{\sqrt{7} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{4} - \frac{\sqrt{7} i}{4} \right)}\right)}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{4} + \frac{\sqrt{7} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{4} + \frac{\sqrt{7} i}{4} \right)}\right)}\right)$$

         /    /        ___\\       /    /        ___\\         /    /        ___\\         /    /        ___\\
         |    |3   I*\/ 7 ||       |    |3   I*\/ 7 ||         |    |3   I*\/ 7 ||         |    |3   I*\/ 7 ||
pi - 2*re|atan|- - -------|| - 2*re|atan|- + -------|| - 2*I*im|atan|- - -------|| - 2*I*im|atan|- + -------||
         \    \4      4   //       \    \4      4   //         \    \4      4   //         \    \4      4   //

$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{4} - \frac{\sqrt{7} i}{4} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{4} + \frac{\sqrt{7} i}{4} \right)}\right)} + \pi - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{4} + \frac{\sqrt{7} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{4} - \frac{\sqrt{7} i}{4} \right)}\right)}$$

Simplify

product

                  /    /        ___\\         /    /        ___\\         /    /        ___\\         /    /        ___\\
pi   5*pi         |    |3   I*\/ 7 ||         |    |3   I*\/ 7 ||         |    |3   I*\/ 7 ||         |    |3   I*\/ 7 ||
-- * ---- * - 2*re|atan|- - -------|| - 2*I*im|atan|- - -------|| * - 2*re|atan|- + -------|| - 2*I*im|atan|- + -------||
6     6           \    \4      4   //         \    \4      4   //         \    \4      4   //         \    \4      4   //

$$\left(\frac{\pi}{6}\right) * \left(\frac{5 \pi}{6}\right) * \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{4} - \frac{\sqrt{7} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{4} - \frac{\sqrt{7} i}{4} \right)}\right)}\right) * \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{4} + \frac{\sqrt{7} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{4} + \frac{\sqrt{7} i}{4} \right)}\right)}\right)$$

      /    /    /        ___\\     /    /        ___\\\ /    /    /        ___\\     /    /        ___\\\
    2 |    |    |3   I*\/ 7 ||     |    |3   I*\/ 7 ||| |    |    |3   I*\/ 7 ||     |    |3   I*\/ 7 |||
5*pi *|I*im|atan|- - -------|| + re|atan|- - -------|||*|I*im|atan|- + -------|| + re|atan|- + -------|||
      \    \    \4      4   //     \    \4      4   /// \    \    \4      4   //     \    \4      4   ///
---------------------------------------------------------------------------------------------------------
                                                    9

$$\frac{5 \pi^{2} \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{4} - \frac{\sqrt{7} i}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{4} - \frac{\sqrt{7} i}{4} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{4} + \frac{\sqrt{7} i}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{4} + \frac{\sqrt{7} i}{4} \right)}\right)}\right)}{9}$$

Simplify

Rapid solution [src]

      pi
x_1 = --
      6

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

Simplify

      5*pi
x_2 = ----
       6

$$x_{2} = \frac{5 \pi}{6}$$

Simplify

            /    /        ___\\         /    /        ___\\
            |    |3   I*\/ 7 ||         |    |3   I*\/ 7 ||
x_3 = - 2*re|atan|- - -------|| - 2*I*im|atan|- - -------||
            \    \4      4   //         \    \4      4   //

$$x_{3} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{4} - \frac{\sqrt{7} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{4} - \frac{\sqrt{7} i}{4} \right)}\right)}$$

Simplify

            /    /        ___\\         /    /        ___\\
            |    |3   I*\/ 7 ||         |    |3   I*\/ 7 ||
x_4 = - 2*re|atan|- + -------|| - 2*I*im|atan|- + -------||
            \    \4      4   //         \    \4      4   //

$$x_{4} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{4} + \frac{\sqrt{7} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{4} + \frac{\sqrt{7} i}{4} \right)}\right)}$$

Simplify

Numerical answer [src]

x1 = -79.0634151153431

x2 = -879.122344229544

x3 = 276.9837522915

x4 = 40.317105721069

x5 = 90.5825881785057

x6 = 75.9218224617533

x7 = 78.0162175641465

x8 = -91.6297857297023

x9 = 38.2227106186758

x10 = -93.7241808320955

x11 = -43.4586983746588

x12 = -9.94837673636768

x13 = 25.6563400043166

x14 = 44.5058959258554

x15 = 15.1843644923507

x16 = 82.2050077689329

x17 = -100.007366139275

x18 = 103.148958792865

x19 = -81.1578102177363

x20 = -6538.17791089596

x21 = -24.60914245312

x22 = 264.417381677141

x23 = -12.0427718387609

x24 = 27.7507351067098

x25 = 34.0339204138894

x26 = -35.081117965086

x27 = 71.733032256967

x28 = -3.66519142918809

x29 = -62.3082542961976

x30 = -60.2138591938044

x31 = 88.4881930761125

x32 = -97.9129710368819

x33 = -18.3259571459405

x34 = -5.75958653158129

x35 = 46.6002910282486

x36 = 84.2994028713261

x37 = 63.3554518473942

x38 = 2.61799387799149

x39 = 31.9395253114962

x40 = -87.4409955249159

x41 = -68.5914396033772

x42 = -16.2315620435473

x43 = -56.025068989018

x44 = 6.80678408277789

x45 = -49.7418836818384

x46 = 50.789081233035

x47 = -53.9306738866248

x48 = 239.284640448423

x49 = 65.4498469497874

x50 = 0.523598775598299

x51 = -47.6474885794452

x51 = -47.6474885794452

The graph

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4/(1-cos^2*x)-(5/sinx)=6 equation

Numerical solution:

The solution