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- La ecuación:
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Ecuación x=(x+1)/2
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Ecuación x^2-14*x+33=0
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Ecuación x^2+6=5x
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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
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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
$$- \left(\sin{\left(a \right)} - \sin{\left(b \right)}\right)^{2} + \left(\cos{\left(a \right)} - \cos{\left(b \right)}\right)^{2} = 0$$
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)))