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Equation:
Equation (x-4)/(x-6)=2
Equation e^x=2
Equation x^2+4*x=21
Equation x^3+x-1=0
Express {x} in terms of y where:
19*x-3*y=-12
17*x-7*y=15
-11*x-6*y=1
14*x+3*y=-4
Derivative of:
4/cosx
Identical expressions
four 9cos^2x+11sinx=4/cosx
49 co sinus of e of squared x plus 11 sinus of x equally 4 divide by co sinus of e of x
four 9 co sinus of e of squared x plus 11 sinus of x equally 4 divide by co sinus of e of x
49cos2x+11sinx=4/cosx
49cos²x+11sinx=4/cosx
49cos to the power of 2x+11sinx=4/cosx
49cos^2x+11sinx=4 divide by cosx
Similar expressions
49cos^2x-11sinx=4/cosx
(sina)^4/(sinx)^2+(cosa)^4/(cosx)^2=1
((2/cos(x))-1)^2+2*((2*sin(x))/(cos(x))^2)^2-4/(cos(x))^4=0

49cos^2x+11sinx=4/cosx equation

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The solution

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      2                    4   
49*cos (x) + 11*sin(x) = ------
                         cos(x)

$$11 \sin{\left(x \right)} + 49 \cos^{2}{\left(x \right)} = \frac{4}{\cos{\left(x \right)}}$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

           /       /    6       5        4        2               \\
x1 = 2*atan\CRootOf\53*x  + 22*x  - 135*x  + 159*x  - 22*x - 45, 0//

$$x_{1} = 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(53 x^{6} + 22 x^{5} - 135 x^{4} + 159 x^{2} - 22 x - 45, 0\right)} \right)}$$

           /       /    6       5        4        2               \\
x2 = 2*atan\CRootOf\53*x  + 22*x  - 135*x  + 159*x  - 22*x - 45, 1//

$$x_{2} = 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(53 x^{6} + 22 x^{5} - 135 x^{4} + 159 x^{2} - 22 x - 45, 1\right)} \right)}$$

         /    /       /    6       5        4        2               \\\         /    /       /    6       5        4        2               \\\
x3 = 2*re\atan\CRootOf\53*x  + 22*x  - 135*x  + 159*x  - 22*x - 45, 2/// + 2*I*im\atan\CRootOf\53*x  + 22*x  - 135*x  + 159*x  - 22*x - 45, 2///

$$x_{3} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(53 x^{6} + 22 x^{5} - 135 x^{4} + 159 x^{2} - 22 x - 45, 2\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(53 x^{6} + 22 x^{5} - 135 x^{4} + 159 x^{2} - 22 x - 45, 2\right)} \right)}\right)}$$

         /    /       /    6       5        4        2               \\\         /    /       /    6       5        4        2               \\\
x4 = 2*re\atan\CRootOf\53*x  + 22*x  - 135*x  + 159*x  - 22*x - 45, 3/// + 2*I*im\atan\CRootOf\53*x  + 22*x  - 135*x  + 159*x  - 22*x - 45, 3///

$$x_{4} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(53 x^{6} + 22 x^{5} - 135 x^{4} + 159 x^{2} - 22 x - 45, 3\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(53 x^{6} + 22 x^{5} - 135 x^{4} + 159 x^{2} - 22 x - 45, 3\right)} \right)}\right)}$$

         /    /       /    6       5        4        2               \\\         /    /       /    6       5        4        2               \\\
x5 = 2*re\atan\CRootOf\53*x  + 22*x  - 135*x  + 159*x  - 22*x - 45, 4/// + 2*I*im\atan\CRootOf\53*x  + 22*x  - 135*x  + 159*x  - 22*x - 45, 4///

$$x_{5} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(53 x^{6} + 22 x^{5} - 135 x^{4} + 159 x^{2} - 22 x - 45, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(53 x^{6} + 22 x^{5} - 135 x^{4} + 159 x^{2} - 22 x - 45, 4\right)} \right)}\right)}$$

         /    /       /    6       5        4        2               \\\         /    /       /    6       5        4        2               \\\
x6 = 2*re\atan\CRootOf\53*x  + 22*x  - 135*x  + 159*x  - 22*x - 45, 5/// + 2*I*im\atan\CRootOf\53*x  + 22*x  - 135*x  + 159*x  - 22*x - 45, 5///

$$x_{6} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(53 x^{6} + 22 x^{5} - 135 x^{4} + 159 x^{2} - 22 x - 45, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(53 x^{6} + 22 x^{5} - 135 x^{4} + 159 x^{2} - 22 x - 45, 5\right)} \right)}\right)}$$

Eq(x6, 2*re(atan(CRootOf(53*x^6 + 22*x^5 - 135*x^4 + 159*x^2 - 22*x - 45, 5))) + 2*i*im(atan(CRootOf(53*x^6 + 22*x^5 - 135*x^4 + 159*x^2 - 22*x - 45, 5))))

Numerical answer [src]

x1 = 64.1204544656937

x2 = -74.1096222922572

x3 = 55.5865531529521

x4 = 5.3210706955154

x5 = -23.8441398348205

x6 = 20.1381573154366

x7 = 32.7045279297958

x8 = -88.9267089121784

x9 = -4.99458391328172

x10 = 26.4213426226162

x11 = -76.3603382978192

x12 = 68.1529237673113

x13 = -80.3928075994368

x14 = -67.8264369850776

x15 = 13.854972008257

x16 = 30.4538119242337

x17 = -99.2423635209755

x18 = -38.6612264547417

x19 = -61.543251677898

x20 = 76.6868250800529

x21 = -26.0948558403825

x22 = -17.5609545276409

x23 = 17.8874413098746

x24 = -82.6435236049988

x25 = 11.604256002695

x26 = 82.9700103872325

x27 = 61.8697384601317

x28 = -32.3780411475621

x29 = 70.4036397728733

x30 = -13.5284852260234

x31 = 7.57178670107746

x32 = -51.2275970691009

x33 = 93.2856649960296

x34 = 2112.43886460624

x35 = -48.9768810635388

x36 = -70.0771529906396

x37 = -55.2600663707184

x38 = 87.00247968885

x39 = -11.2777692204613

x40 = 51.5540838513346

x41 = -63.7939676834601

x42 = 38.9877132369754

x43 = 24.1706266170542

x44 = 99.5688503032092

x45 = 74.4361090744909

x46 = -0.962114611664186

x47 = -30.1273251420001

x48 = -57.5107823762805

x49 = 80.7192943816704

x50 = -92.9591782137959

x51 = -19.8116705332029

x52 = 36.7369972314133

x52 = 36.7369972314133

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49cos^2x+11sinx=4/cosx equation

Numerical solution:

The solution