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La ecuación:
Ecuación 4^x-3*2^x+2=0
Ecuación (x-2)/(x-7)=5/8
Ecuación 4/(x-4)=-5
Ecuación (x-6)^2=-24*x
Expresar {x} en función de y en la ecuación:
20*x+5*y=-3
-11*x-14*y=-3
20*x+18*y=-9
-2*x+2*y=4
Expresiones idénticas
dos sin^2(x)-sqrt(tres)sin(x)/2cos(x)+ uno = cero
2 seno de al cuadrado (x) menos raíz cuadrada de (3) seno de (x) dividir por 2 coseno de (x) más 1 es igual a 0
dos seno de al cuadrado (x) menos raíz cuadrada de (tres) seno de (x) dividir por 2 coseno de (x) más uno es igual a cero
2sin^2(x)-√(3)sin(x)/2cos(x)+1=0
2sin2(x)-sqrt(3)sin(x)/2cos(x)+1=0
2sin2x-sqrt3sinx/2cosx+1=0
2sin²(x)-sqrt(3)sin(x)/2cos(x)+1=0
2sin en el grado 2(x)-sqrt(3)sin(x)/2cos(x)+1=0
2sin^2x-sqrt3sinx/2cosx+1=0
2sin^2(x)-sqrt(3)sin(x)/2cos(x)+1=O
2sin^2(x)-sqrt(3)sin(x) dividir por 2cos(x)+1=0
Expresiones semejantes
2sin^2(x)+sqrt(3)sin(x)/2cos(x)+1=0
2sin^2(x)-sqrt(3)sin(x)/2cos(x)-1=0
2sin^2(x)-sqrt(3)sinx/2cosx+1=0
Expresiones con funciones
Raíz cuadrada sqrt
sqrt(x)=1
sqrt(12+x)-sqrt(1-x)=1
sqrt(12-x)=x
sqrt(x-2)+sqrt(y-2)=2
sqrt(2-x)+sqrt(-x-1)=sqrt(-5*x-7)
Seno sin
sin(x)=1,5
sin2x=1
sin(x)=pi
sin(x)=a
sin(3*x)=-1

2sin^2(x)-sqrt(3)sin(x)/2cos(x)+1=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

              ___                      
     2      \/ 3 *sin(x)               
2*sin (x) - ------------*cos(x) + 1 = 0
                 2

\left(- \frac{\sqrt{3} \sin{\left(x \right)}}{2} \cos{\left(x \right)} + 2 \sin^{2}{\left(x \right)}\right) + 1 = 0

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

         /    /                   __________________            \\         /    /                   __________________            \\
         |    |    ___     ___   /             ____          ___||         |    |    ___     ___   /             ____          ___||
         |    |  \/ 3    \/ 2 *\/  -13 - 3*I*\/ 15     3*I*\/ 5 ||         |    |  \/ 3    \/ 2 *\/  -13 - 3*I*\/ 15     3*I*\/ 5 ||
x1 = 2*re|atan|- ----- + --------------------------- + ---------|| + 2*I*im|atan|- ----- + --------------------------- + ---------||
         \    \    4                  4                    4    //         \    \    4                  4                    4    //

x_{1} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)}

           /    /                 __________________            \\         /    /                 __________________            \\
           |    |  ___     ___   /             ____          ___||         |    |  ___     ___   /             ____          ___||
           |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||         |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||
x2 = - 2*re|atan|----- - --------------------------- + ---------|| - 2*I*im|atan|----- - --------------------------- + ---------||
           \    \  4                  4                    4    //         \    \  4                  4                    4    //

x_{2} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)}

           /    /                 __________________            \\         /    /                 __________________            \\
           |    |  ___     ___   /             ____          ___||         |    |  ___     ___   /             ____          ___||
           |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||         |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||
x3 = - 2*re|atan|----- + --------------------------- + ---------|| - 2*I*im|atan|----- + --------------------------- + ---------||
           \    \  4                  4                    4    //         \    \  4                  4                    4    //

x_{3} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)}

           /    /                             __________________\\         /    /                             __________________\\
           |    |  ___         ___     ___   /             ____ ||         |    |  ___         ___     ___   /             ____ ||
           |    |\/ 3    3*I*\/ 5    \/ 2 *\/  -13 - 3*I*\/ 15  ||         |    |\/ 3    3*I*\/ 5    \/ 2 *\/  -13 - 3*I*\/ 15  ||
x4 = - 2*re|atan|----- - --------- + ---------------------------|| - 2*I*im|atan|----- - --------- + ---------------------------||
           \    \  4         4                    4             //         \    \  4         4                    4             //

x_{4} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{3 \sqrt{5} i}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{3 \sqrt{5} i}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} \right)}\right)}

x4 = -2*re(atan(sqrt(3)/4 - 3*sqrt(5)*i/4 + sqrt(2)*sqrt(-13 - 3*sqrt(15)*i)/4)) - 2*i*im(atan(sqrt(3)/4 - 3*sqrt(5)*i/4 + sqrt(2)*sqrt(-13 - 3*sqrt(15)*i)/4))

Suma y producto de raíces [src]

suma

    /    /                   __________________            \\         /    /                   __________________            \\         /    /                 __________________            \\         /    /                 __________________            \\         /    /                 __________________            \\         /    /                 __________________            \\         /    /                             __________________\\         /    /                             __________________\\
    |    |    ___     ___   /             ____          ___||         |    |    ___     ___   /             ____          ___||         |    |  ___     ___   /             ____          ___||         |    |  ___     ___   /             ____          ___||         |    |  ___     ___   /             ____          ___||         |    |  ___     ___   /             ____          ___||         |    |  ___         ___     ___   /             ____ ||         |    |  ___         ___     ___   /             ____ ||
    |    |  \/ 3    \/ 2 *\/  -13 - 3*I*\/ 15     3*I*\/ 5 ||         |    |  \/ 3    \/ 2 *\/  -13 - 3*I*\/ 15     3*I*\/ 5 ||         |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||         |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||         |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||         |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||         |    |\/ 3    3*I*\/ 5    \/ 2 *\/  -13 - 3*I*\/ 15  ||         |    |\/ 3    3*I*\/ 5    \/ 2 *\/  -13 - 3*I*\/ 15  ||
2*re|atan|- ----- + --------------------------- + ---------|| + 2*I*im|atan|- ----- + --------------------------- + ---------|| + - 2*re|atan|----- - --------------------------- + ---------|| - 2*I*im|atan|----- - --------------------------- + ---------|| + - 2*re|atan|----- + --------------------------- + ---------|| - 2*I*im|atan|----- + --------------------------- + ---------|| + - 2*re|atan|----- - --------- + ---------------------------|| - 2*I*im|atan|----- - --------- + ---------------------------||
    \    \    4                  4                    4    //         \    \    4                  4                    4    //         \    \  4                  4                    4    //         \    \  4                  4                    4    //         \    \  4                  4                    4    //         \    \  4                  4                    4    //         \    \  4         4                    4             //         \    \  4         4                    4             //

\left(\left(\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)}\right)\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)}\right)\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{3 \sqrt{5} i}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{3 \sqrt{5} i}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} \right)}\right)}\right)

      /    /                             __________________\\       /    /                 __________________            \\       /    /                 __________________            \\       /    /                   __________________            \\         /    /                             __________________\\         /    /                 __________________            \\         /    /                 __________________            \\         /    /                   __________________            \\
      |    |  ___         ___     ___   /             ____ ||       |    |  ___     ___   /             ____          ___||       |    |  ___     ___   /             ____          ___||       |    |    ___     ___   /             ____          ___||         |    |  ___         ___     ___   /             ____ ||         |    |  ___     ___   /             ____          ___||         |    |  ___     ___   /             ____          ___||         |    |    ___     ___   /             ____          ___||
      |    |\/ 3    3*I*\/ 5    \/ 2 *\/  -13 - 3*I*\/ 15  ||       |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||       |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||       |    |  \/ 3    \/ 2 *\/  -13 - 3*I*\/ 15     3*I*\/ 5 ||         |    |\/ 3    3*I*\/ 5    \/ 2 *\/  -13 - 3*I*\/ 15  ||         |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||         |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||         |    |  \/ 3    \/ 2 *\/  -13 - 3*I*\/ 15     3*I*\/ 5 ||
- 2*re|atan|----- - --------- + ---------------------------|| - 2*re|atan|----- - --------------------------- + ---------|| - 2*re|atan|----- + --------------------------- + ---------|| + 2*re|atan|- ----- + --------------------------- + ---------|| - 2*I*im|atan|----- - --------- + ---------------------------|| - 2*I*im|atan|----- - --------------------------- + ---------|| - 2*I*im|atan|----- + --------------------------- + ---------|| + 2*I*im|atan|- ----- + --------------------------- + ---------||
      \    \  4         4                    4             //       \    \  4                  4                    4    //       \    \  4                  4                    4    //       \    \    4                  4                    4    //         \    \  4         4                    4             //         \    \  4                  4                    4    //         \    \  4                  4                    4    //         \    \    4                  4                    4    //

- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{3 \sqrt{5} i}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{3 \sqrt{5} i}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)}

producto

/    /    /                   __________________            \\         /    /                   __________________            \\\ /      /    /                 __________________            \\         /    /                 __________________            \\\ /      /    /                 __________________            \\         /    /                 __________________            \\\ /      /    /                             __________________\\         /    /                             __________________\\\
|    |    |    ___     ___   /             ____          ___||         |    |    ___     ___   /             ____          ___||| |      |    |  ___     ___   /             ____          ___||         |    |  ___     ___   /             ____          ___||| |      |    |  ___     ___   /             ____          ___||         |    |  ___     ___   /             ____          ___||| |      |    |  ___         ___     ___   /             ____ ||         |    |  ___         ___     ___   /             ____ |||
|    |    |  \/ 3    \/ 2 *\/  -13 - 3*I*\/ 15     3*I*\/ 5 ||         |    |  \/ 3    \/ 2 *\/  -13 - 3*I*\/ 15     3*I*\/ 5 ||| |      |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||         |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||| |      |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||         |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||| |      |    |\/ 3    3*I*\/ 5    \/ 2 *\/  -13 - 3*I*\/ 15  ||         |    |\/ 3    3*I*\/ 5    \/ 2 *\/  -13 - 3*I*\/ 15  |||
|2*re|atan|- ----- + --------------------------- + ---------|| + 2*I*im|atan|- ----- + --------------------------- + ---------|||*|- 2*re|atan|----- - --------------------------- + ---------|| - 2*I*im|atan|----- - --------------------------- + ---------|||*|- 2*re|atan|----- + --------------------------- + ---------|| - 2*I*im|atan|----- + --------------------------- + ---------|||*|- 2*re|atan|----- - --------- + ---------------------------|| - 2*I*im|atan|----- - --------- + ---------------------------|||
\    \    \    4                  4                    4    //         \    \    4                  4                    4    /// \      \    \  4                  4                    4    //         \    \  4                  4                    4    /// \      \    \  4                  4                    4    //         \    \  4                  4                    4    /// \      \    \  4         4                    4             //         \    \  4         4                    4             ///

\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{3 \sqrt{5} i}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{3 \sqrt{5} i}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} \right)}\right)}\right)

    /    /    /                   __________________            \\     /    /                   __________________            \\\ /    /    /                             __________________\\     /    /                             __________________\\\ /    /    /                 __________________            \\     /    /                 __________________            \\\ /    /    /                 __________________            \\     /    /                 __________________            \\\
    |    |    |    ___     ___   /             ____          ___||     |    |    ___     ___   /             ____          ___||| |    |    |  ___         ___     ___   /             ____ ||     |    |  ___         ___     ___   /             ____ ||| |    |    |  ___     ___   /             ____          ___||     |    |  ___     ___   /             ____          ___||| |    |    |  ___     ___   /             ____          ___||     |    |  ___     ___   /             ____          ___|||
    |    |    |  \/ 3    \/ 2 *\/  -13 - 3*I*\/ 15     3*I*\/ 5 ||     |    |  \/ 3    \/ 2 *\/  -13 - 3*I*\/ 15     3*I*\/ 5 ||| |    |    |\/ 3    3*I*\/ 5    \/ 2 *\/  -13 - 3*I*\/ 15  ||     |    |\/ 3    3*I*\/ 5    \/ 2 *\/  -13 - 3*I*\/ 15  ||| |    |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||     |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||| |    |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 ||     |    |\/ 3    \/ 2 *\/  -13 + 3*I*\/ 15     3*I*\/ 5 |||
-16*|I*im|atan|- ----- + --------------------------- + ---------|| + re|atan|- ----- + --------------------------- + ---------|||*|I*im|atan|----- - --------- + ---------------------------|| + re|atan|----- - --------- + ---------------------------|||*|I*im|atan|----- - --------------------------- + ---------|| + re|atan|----- - --------------------------- + ---------|||*|I*im|atan|----- + --------------------------- + ---------|| + re|atan|----- + --------------------------- + ---------|||
    \    \    \    4                  4                    4    //     \    \    4                  4                    4    /// \    \    \  4         4                    4             //     \    \  4         4                    4             /// \    \    \  4                  4                    4    //     \    \  4                  4                    4    /// \    \    \  4                  4                    4    //     \    \  4                  4                    4    ///

- 16 \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{-13 + 3 \sqrt{15} i}}{4} + \frac{3 \sqrt{5} i}{4} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{3 \sqrt{5} i}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{3}}{4} - \frac{3 \sqrt{5} i}{4} + \frac{\sqrt{2} \sqrt{-13 - 3 \sqrt{15} i}}{4} \right)}\right)}\right)

-16*(i*im(atan(-sqrt(3)/4 + sqrt(2)*sqrt(-13 - 3*i*sqrt(15))/4 + 3*i*sqrt(5)/4)) + re(atan(-sqrt(3)/4 + sqrt(2)*sqrt(-13 - 3*i*sqrt(15))/4 + 3*i*sqrt(5)/4)))*(i*im(atan(sqrt(3)/4 - 3*i*sqrt(5)/4 + sqrt(2)*sqrt(-13 - 3*i*sqrt(15))/4)) + re(atan(sqrt(3)/4 - 3*i*sqrt(5)/4 + sqrt(2)*sqrt(-13 - 3*i*sqrt(15))/4)))*(i*im(atan(sqrt(3)/4 - sqrt(2)*sqrt(-13 + 3*i*sqrt(15))/4 + 3*i*sqrt(5)/4)) + re(atan(sqrt(3)/4 - sqrt(2)*sqrt(-13 + 3*i*sqrt(15))/4 + 3*i*sqrt(5)/4)))*(i*im(atan(sqrt(3)/4 + sqrt(2)*sqrt(-13 + 3*i*sqrt(15))/4 + 3*i*sqrt(5)/4)) + re(atan(sqrt(3)/4 + sqrt(2)*sqrt(-13 + 3*i*sqrt(15))/4 + 3*i*sqrt(5)/4)))

Respuesta numérica [src]

x1 = 0.204318927548796 + 0.608092969586509*i

x2 = 0.204318927548796 - 0.608092969586509*i

x3 = -2.937273726041 - 0.608092969586509*i

x4 = -2.937273726041 + 0.608092969586509*i

x4 = -2.937273726041 + 0.608092969586509*i

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2sin^2(x)-sqrt(3)sin(x)/2cos(x)+1=0 la ecuación

Solución numérica:

Solución