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La ecuación:
Ecuación 56/x=(10+6)/2
Ecuación 15-4(7-x)=11
Ecuación 3^8-x=27
Ecuación 6,4(y-12,8)=3,2
Expresar {x} en función de y en la ecuación:
20*x+7*y=-9
-13*x-10*y=5
15*x+7*y=2
20*x+9*y=17
Expresiones idénticas
(cosa-cosb)^ dos -(sina-sinb)^ dos
( coseno de a menos coseno de b) al cuadrado menos ( seno de a menos seno de b) al cuadrado
( coseno de a menos coseno de b) en el grado dos menos ( seno de a menos seno de b) en el grado dos
(cosa-cosb)2-(sina-sinb)2
cosa-cosb2-sina-sinb2
(cosa-cosb)²-(sina-sinb)²
(cosa-cosb) en el grado 2-(sina-sinb) en el grado 2
cosa-cosb^2-sina-sinb^2
Expresiones semejantes
(cosa-cosb)^2+(sina-sinb)^2
(cosa-cosb)^2-(sina+sinb)^2
(cosa+cosb)^2-(sina-sinb)^2

(cosa-cosb)^2-(sina-sinb)^2 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

                 2                    2    
(cos(a) - cos(b))  - (sin(a) - sin(b))  = 0

- \left(\sin{\left(a \right)} - \sin{\left(b \right)}\right)^{2} + \left(\cos{\left(a \right)} - \cos{\left(b \right)}\right)^{2} = 0

Simplificar

Gráfica

Suma y producto de raíces [src]

suma

    /    /        /a\\\         /    /        /a\\\         /    /        /a\\\         /    /        /a\\\                                            
    |    | 1 + tan|-|||         |    | 1 + tan|-|||         |    |-1 + tan|-|||         |    |-1 + tan|-|||                                            
    |    |        \2/||         |    |        \2/||         |    |        \2/||         |    |        \2/||       /    /   /a\\\         /    /   /a\\\
2*re|atan|-----------|| + 2*I*im|atan|-----------|| + - 2*re|atan|-----------|| - 2*I*im|atan|-----------|| + 2*re|atan|tan|-||| + 2*I*im|atan|tan|-|||
    |    |        /a\||         |    |        /a\||         |    |        /a\||         |    |        /a\||       \    \   \2///         \    \   \2///
    |    |-1 + tan|-|||         |    |-1 + tan|-|||         |    | 1 + tan|-|||         |    | 1 + tan|-|||                                            
    \    \        \2///         \    \        \2///         \    \        \2///         \    \        \2///

\left(\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} + 1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} + 1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)}\right)}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} - 1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} - 1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\tan{\left(\frac{a}{2} \right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\tan{\left(\frac{a}{2} \right)} \right)}\right)}\right)

      /    /        /a\\\       /    /        /a\\\                              /    /        /a\\\         /    /        /a\\\                       
      |    |-1 + tan|-|||       |    | 1 + tan|-|||                              |    |-1 + tan|-|||         |    | 1 + tan|-|||                       
      |    |        \2/||       |    |        \2/||       /    /   /a\\\         |    |        \2/||         |    |        \2/||         /    /   /a\\\
- 2*re|atan|-----------|| + 2*re|atan|-----------|| + 2*re|atan|tan|-||| - 2*I*im|atan|-----------|| + 2*I*im|atan|-----------|| + 2*I*im|atan|tan|-|||
      |    |        /a\||       |    |        /a\||       \    \   \2///         |    |        /a\||         |    |        /a\||         \    \   \2///
      |    | 1 + tan|-|||       |    |-1 + tan|-|||                              |    | 1 + tan|-|||         |    |-1 + tan|-|||                       
      \    \        \2///       \    \        \2///                              \    \        \2///         \    \        \2///

2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} + 1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} - 1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\tan{\left(\frac{a}{2} \right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} + 1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} - 1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\tan{\left(\frac{a}{2} \right)} \right)}\right)}

producto

/    /    /        /a\\\         /    /        /a\\\\ /      /    /        /a\\\         /    /        /a\\\\                                            
|    |    | 1 + tan|-|||         |    | 1 + tan|-|||| |      |    |-1 + tan|-|||         |    |-1 + tan|-||||                                            
|    |    |        \2/||         |    |        \2/||| |      |    |        \2/||         |    |        \2/||| /    /    /   /a\\\         /    /   /a\\\\
|2*re|atan|-----------|| + 2*I*im|atan|-----------|||*|- 2*re|atan|-----------|| - 2*I*im|atan|-----------|||*|2*re|atan|tan|-||| + 2*I*im|atan|tan|-||||
|    |    |        /a\||         |    |        /a\||| |      |    |        /a\||         |    |        /a\||| \    \    \   \2///         \    \   \2////
|    |    |-1 + tan|-|||         |    |-1 + tan|-|||| |      |    | 1 + tan|-|||         |    | 1 + tan|-||||                                            
\    \    \        \2///         \    \        \2//// \      \    \        \2///         \    \        \2////

\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} + 1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} + 1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} - 1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} - 1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\tan{\left(\frac{a}{2} \right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\tan{\left(\frac{a}{2} \right)} \right)}\right)}\right)

   /    /    /        /a\\\     /    /        /a\\\\ /    /    /        /a\\\     /    /        /a\\\\                                        
   |    |    |-1 + tan|-|||     |    |-1 + tan|-|||| |    |    | 1 + tan|-|||     |    | 1 + tan|-||||                                        
   |    |    |        \2/||     |    |        \2/||| |    |    |        \2/||     |    |        \2/||| /    /    /   /a\\\     /    /   /a\\\\
-8*|I*im|atan|-----------|| + re|atan|-----------|||*|I*im|atan|-----------|| + re|atan|-----------|||*|I*im|atan|tan|-||| + re|atan|tan|-||||
   |    |    |        /a\||     |    |        /a\||| |    |    |        /a\||     |    |        /a\||| \    \    \   \2///     \    \   \2////
   |    |    | 1 + tan|-|||     |    | 1 + tan|-|||| |    |    |-1 + tan|-|||     |    |-1 + tan|-||||                                        
   \    \    \        \2///     \    \        \2//// \    \    \        \2///     \    \        \2////

- 8 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} + 1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} + 1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} - 1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} - 1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\tan{\left(\frac{a}{2} \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\tan{\left(\frac{a}{2} \right)} \right)}\right)}\right)

-8*(i*im(atan((-1 + tan(a/2))/(1 + tan(a/2)))) + re(atan((-1 + tan(a/2))/(1 + tan(a/2)))))*(i*im(atan((1 + tan(a/2))/(-1 + tan(a/2)))) + re(atan((1 + tan(a/2))/(-1 + tan(a/2)))))*(i*im(atan(tan(a/2))) + re(atan(tan(a/2))))

Respuesta rápida [src]

         /    /        /a\\\         /    /        /a\\\
         |    | 1 + tan|-|||         |    | 1 + tan|-|||
         |    |        \2/||         |    |        \2/||
b1 = 2*re|atan|-----------|| + 2*I*im|atan|-----------||
         |    |        /a\||         |    |        /a\||
         |    |-1 + tan|-|||         |    |-1 + tan|-|||
         \    \        \2///         \    \        \2///

b_{1} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} + 1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} + 1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)}\right)}

           /    /        /a\\\         /    /        /a\\\
           |    |-1 + tan|-|||         |    |-1 + tan|-|||
           |    |        \2/||         |    |        \2/||
b2 = - 2*re|atan|-----------|| - 2*I*im|atan|-----------||
           |    |        /a\||         |    |        /a\||
           |    | 1 + tan|-|||         |    | 1 + tan|-|||
           \    \        \2///         \    \        \2///

b_{2} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} - 1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{a}{2} \right)} - 1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)}\right)}

         /    /   /a\\\         /    /   /a\\\
b3 = 2*re|atan|tan|-||| + 2*I*im|atan|tan|-|||
         \    \   \2///         \    \   \2///

b_{3} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\tan{\left(\frac{a}{2} \right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\tan{\left(\frac{a}{2} \right)} \right)}\right)}

b3 = 2*re(atan(tan(a/2))) + 2*i*im(atan(tan(a/2)))

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Expresiones idénticas

Expresiones semejantes

(cosa-cosb)^2-(sina-sinb)^2 la ecuación

Solución numérica:

Solución