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1/(6tan^6(x))= 1/(6sec^6(x))

Solución

\frac{1}{6 tan ^{6} ( x )} = \frac{1}{6 sec ^{6} ( x )}

Solución

Sin soluci \overset{o}{ˊ} n para x \in R

Pasos de solución

\frac{1}{6 tan ^{6} ( x )} = \frac{1}{6 sec ^{6} ( x )}

Restar

\frac{1}{6 sec ^{6} ( x )}

de ambos lados

\frac{1}{6 tan ^{6} ( x )} - \frac{1}{6 sec ^{6} ( x )} = 0

Simplificar

\frac{1}{6 tan ^{6} ( x )} - \frac{1}{6 sec ^{6} ( x )} : \frac{sec ^{6} ( x ) - tan ^{6} ( x )}{6 tan ^{6} ( x ) sec ^{6} ( x )}

\frac{1}{6 tan ^{6} ( x )} - \frac{1}{6 sec ^{6} ( x )}

Mínimo común múltiplo de

6 tan^{6} (x), 6 sec^{6} (x) : 6 tan^{6} (x) sec^{6} (x)

6 tan^{6} (x), 6 sec^{6} (x)

Mínimo común múltiplo (MCM)

Mínimo común múltiplo de

6, 6 : 6

6, 6

Mínimo común múltiplo (MCM)

Descomposición en factores primos de

6 : 2 \cdot 3

6

6

divida por

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

son números primos, por lo tanto, no se pueden factorizar mas

= 2 \cdot 3

Descomposición en factores primos de

6 : 2 \cdot 3

6

6

divida por

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

son números primos, por lo tanto, no se pueden factorizar mas

= 2 \cdot 3

Multiplicar cada factor el mayor número de veces que ocurra en cualquier

6

6

= 2 \cdot 3

Multiplicar los numeros:

2 \cdot 3 = 6

= 6

Calcular una expresión que este compuesta de factores que aparezcan tanto en

6 tan^{6} (x)

6 sec^{6} (x)

= 6 tan^{6} (x) sec^{6} (x)

Reescribir las fracciones basandose en el mínimo común denominador

Multiplicar cada numerador por la misma cantidad necesaria para multiplicar el denominador correspondiente y convertirlo en el mínimo común denominador

Para

\frac{1}{6 tan ^{6} ( x )} :

multiplicar el denominador y el numerador por

sec^{6} (x)

\frac{1}{6 tan ^{6} ( x )} = \frac{1 \cdot sec ^{6} ( x )}{6 tan ^{6} ( x ) sec ^{6} ( x )} = \frac{sec ^{6} ( x )}{6 tan ^{6} ( x ) sec ^{6} ( x )}

Para

\frac{1}{6 sec ^{6} ( x )} :

multiplicar el denominador y el numerador por

tan^{6} (x)

\frac{1}{6 sec ^{6} ( x )} = \frac{1 \cdot tan ^{6} ( x )}{6 sec ^{6} ( x ) tan ^{6} ( x )} = \frac{tan ^{6} ( x )}{6 tan ^{6} ( x ) sec ^{6} ( x )}

= \frac{sec ^{6} ( x )}{6 tan ^{6} ( x ) sec ^{6} ( x )} - \frac{tan ^{6} ( x )}{6 tan ^{6} ( x ) sec ^{6} ( x )}

Ya que los denominadores son iguales, combinar las fracciones:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{sec ^{6} ( x ) - tan ^{6} ( x )}{6 tan ^{6} ( x ) sec ^{6} ( x )}

\frac{sec ^{6} ( x ) - tan ^{6} ( x )}{6 tan ^{6} ( x ) sec ^{6} ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

sec^{6} (x) - tan^{6} (x) = 0

Factorizar

sec^{6} (x) - tan^{6} (x) : (sec (x) + tan (x)) (sec^{2} (x) - sec (x) tan (x) + tan^{2} (x)) (sec (x) - tan (x)) (sec^{2} (x) + sec (x) tan (x) + tan^{2} (x))

sec^{6} (x) - tan^{6} (x)

Reescribir

sec^{6} (x) - tan^{6} (x)

como

(sec^{3} (x))^{2} - (tan^{3} (x))^{2}

sec^{6} (x) - tan^{6} (x)

Aplicar las leyes de los exponentes:

a^{b c} = (a^{b})^{c}

sec^{6} (x) = (sec^{3} (x))^{2}

= (sec^{3} (x))^{2} - tan^{6} (x)

Aplicar las leyes de los exponentes:

a^{b c} = (a^{b})^{c}

tan^{6} (x) = (tan^{3} (x))^{2}

= (sec^{3} (x))^{2} - (tan^{3} (x))^{2}

= (sec^{3} (x))^{2} - (tan^{3} (x))^{2}

Aplicar la siguiente regla para binomios al cuadrado:

x^{2} - y^{2} = (x + y) (x - y)

(sec^{3} (x))^{2} - (tan^{3} (x))^{2} = (sec^{3} (x) + tan^{3} (x)) (sec^{3} (x) - tan^{3} (x))

= (sec^{3} (x) + tan^{3} (x)) (sec^{3} (x) - tan^{3} (x))

Factorizar

sec^{3} (x) + tan^{3} (x) : (sec (x) + tan (x)) (sec^{2} (x) - sec (x) tan (x) + tan^{2} (x))

sec^{3} (x) + tan^{3} (x)

Aplicar la siguiente regla de productos notables (Suma de cubos):

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

sec^{3} (x) + tan^{3} (x) = (sec (x) + tan (x)) (sec^{2} (x) - sec (x) tan (x) + tan^{2} (x))

= (sec (x) + tan (x)) (sec^{2} (x) - sec (x) tan (x) + tan^{2} (x))

= (sec (x) + tan (x)) (sec^{2} (x) - sec (x) tan (x) + tan^{2} (x)) (sec^{3} (x) - tan^{3} (x))

Factorizar

sec^{3} (x) - tan^{3} (x) : (sec (x) - tan (x)) (sec^{2} (x) + sec (x) tan (x) + tan^{2} (x))

sec^{3} (x) - tan^{3} (x)

Aplicar la siguiente regla de productos notables (Diferencia de cubos):

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

sec^{3} (x) - tan^{3} (x) = (sec (x) - tan (x)) (sec^{2} (x) + sec (x) tan (x) + tan^{2} (x))

= (sec (x) - tan (x)) (sec^{2} (x) + sec (x) tan (x) + tan^{2} (x))

= (sec (x) + tan (x)) (sec^{2} (x) - sec (x) tan (x) + tan^{2} (x)) (sec (x) - tan (x)) (sec^{2} (x) + sec (x) tan (x) + tan^{2} (x))

(sec (x) + tan (x)) (sec^{2} (x) - sec (x) tan (x) + tan^{2} (x)) (sec (x) - tan (x)) (sec^{2} (x) + sec (x) tan (x) + tan^{2} (x)) = 0

Re-escribir usando identidades trigonométricas

(sec (x) + tan (x)) (sec^{2} (x) - sec (x) tan (x) + tan^{2} (x)) (sec (x) - tan (x)) (sec^{2} (x) + sec (x) tan (x) + tan^{2} (x))

(sec (x) + tan (x)) (sec (x) - tan (x)) = 1

(sec (x) + tan (x)) (sec (x) - tan (x))

Expandir

(sec (x) + tan (x)) (sec (x) - tan (x)) : sec^{2} (x) - tan^{2} (x)

(sec (x) + tan (x)) (sec (x) - tan (x))

Aplicar la siguiente regla para binomios al cuadrado:

(a + b) (a - b) = a^{2} - b^{2}

a = sec (x), b = tan (x)

= sec^{2} (x) - tan^{2} (x)

= sec^{2} (x) - tan^{2} (x)

Utilizar la identidad pitagórica:

sec^{2} (x) = tan^{2} (x) + 1

sec^{2} (x) - tan^{2} (x) = 1

= 1

= 1 \cdot (sec^{2} (x) + tan^{2} (x) + sec (x) tan (x)) (sec^{2} (x) + tan^{2} (x) - sec (x) tan (x))

Simplificar

1 \cdot (sec^{2} (x) + tan^{2} (x) + sec (x) tan (x)) (sec^{2} (x) + tan^{2} (x) - sec (x) tan (x)) : (sec^{2} (x) + tan^{2} (x) + sec (x) tan (x)) (sec^{2} (x) + tan^{2} (x) - sec (x) tan (x))

1 \cdot (sec^{2} (x) + tan^{2} (x) + sec (x) tan (x)) (sec^{2} (x) + tan^{2} (x) - sec (x) tan (x))

Multiplicar:

1 \cdot (sec^{2} (x) + tan^{2} (x) + sec (x) tan (x)) = (sec^{2} (x) + tan^{2} (x) + sec (x) tan (x))

= (sec^{2} (x) + tan^{2} (x) + sec (x) tan (x)) (sec^{2} (x) + tan^{2} (x) - sec (x) tan (x))

= (sec^{2} (x) + tan^{2} (x) + sec (x) tan (x)) (sec^{2} (x) + tan^{2} (x) - sec (x) tan (x))

(sec^{2} (x) + tan^{2} (x) + sec (x) tan (x)) (sec^{2} (x) + tan^{2} (x) - sec (x) tan (x)) = 0

Resolver cada parte por separado

sec^{2} (x) + tan^{2} (x) + sec (x) tan (x) = 0 or sec^{2} (x) + tan^{2} (x) - sec (x) tan (x) = 0

sec^{2} (x) + tan^{2} (x) + sec (x) tan (x) = 0 :

Sin solución

sec^{2} (x) + tan^{2} (x) + sec (x) tan (x) = 0

Expresar con seno, coseno

sec^{2} (x) + tan^{2} (x) + sec (x) tan (x)

Utilizar la identidad trigonométrica básica:

sec (x) = \frac{1}{cos ( x )}

= (\frac{1}{cos ( x )})^{2} + tan^{2} (x) + \frac{1}{cos ( x )} tan (x)

Utilizar la identidad trigonométrica básica:

tan (x) = \frac{sin ( x )}{cos ( x )}

= (\frac{1}{cos ( x )})^{2} + (\frac{sin ( x )}{cos ( x )})^{2} + \frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Simplificar

(\frac{1}{cos ( x )})^{2} + (\frac{sin ( x )}{cos ( x )})^{2} + \frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )} : \frac{1 + sin ^{2} ( x ) + sin ( x )}{cos ^{2} ( x )}

(\frac{1}{cos ( x )})^{2} + (\frac{sin ( x )}{cos ( x )})^{2} + \frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )}

(\frac{1}{cos ( x )})^{2} = \frac{1}{cos ^{2} ( x )}

(\frac{1}{cos ( x )})^{2}

Aplicar las leyes de los exponentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{cos ^{2} ( x )}

Aplicar la regla

1^{a} = 1

1^{2} = 1

= \frac{1}{cos ^{2} ( x )}

(\frac{sin ( x )}{cos ( x )})^{2} = \frac{sin ^{2} ( x )}{cos ^{2} ( x )}

(\frac{sin ( x )}{cos ( x )})^{2}

Aplicar las leyes de los exponentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{sin ^{2} ( x )}{cos ^{2} ( x )}

\frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )} = \frac{sin ( x )}{cos ^{2} ( x )}

\frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Multiplicar fracciones:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot sin ( x )}{cos ( x ) cos ( x )}

Multiplicar:

1 \cdot sin (x) = sin (x)

= \frac{sin ( x )}{cos ( x ) cos ( x )}

cos (x) cos (x) = cos^{2} (x)

cos (x) cos (x)

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

cos (x) cos (x) = cos^{1 + 1} (x)

= cos^{1 + 1} (x)

Sumar:

1 + 1 = 2

= cos^{2} (x)

= \frac{sin ( x )}{cos ^{2} ( x )}

= \frac{1}{cos ^{2} ( x )} + \frac{sin ^{2} ( x )}{cos ^{2} ( x )} + \frac{sin ( x )}{cos ^{2} ( x )}

Aplicar la regla

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{1 + sin ^{2} ( x ) + sin ( x )}{cos ^{2} ( x )}

= \frac{1 + sin ^{2} ( x ) + sin ( x )}{cos ^{2} ( x )}

\frac{1 + sin ( x ) + sin ^{2} ( x )}{cos ^{2} ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

1 + sin (x) + sin^{2} (x) = 0

Usando el método de sustitución

1 + sin (x) + sin^{2} (x) = 0

Sea:

sin (x) = u

1 + u + u^{2} = 0

1 + u + u^{2} = 0 : u = - \frac{1}{2} + i \frac{3}{2}, u = - \frac{1}{2} - i \frac{3}{2}

1 + u + u^{2} = 0

Escribir en la forma binómica

a x^{2} + b x + c = 0

u^{2} + u + 1 = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

u^{2} + u + 1 = 0

Formula general para ecuaciones de segundo grado:

Para

a = 1, b = 1, c = 1

u_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot 1}{2 \cdot 1}

u_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot 1}{2 \cdot 1}

Simplificar

1^{2} - 4 \cdot 1 \cdot 1 : 3 i

1^{2} - 4 \cdot 1 \cdot 1

Aplicar la regla

1^{a} = 1

1^{2} = 1

= 1 - 4 \cdot 1 \cdot 1

Multiplicar los numeros:

4 \cdot 1 \cdot 1 = 4

= 1 - 4

Restar:

1 - 4 = - 3

= - 3

Aplicar las leyes de los exponentes:

- a = - 1 a

- 3 = - 1 3

= - 1 3

Aplicar las propiedades de los numeros imaginarios:

- 1 = i

= 3 i

u_{1, 2} = \frac{- 1 \pm 3 i}{2 \cdot 1}

Separar las soluciones

u_{1} = \frac{- 1 + 3 i}{2 \cdot 1}, u_{2} = \frac{- 1 - 3 i}{2 \cdot 1}

u = \frac{- 1 + 3 i}{2 \cdot 1} : - \frac{1}{2} + i \frac{3}{2}

\frac{- 1 + 3 i}{2 \cdot 1}

Multiplicar los numeros:

2 \cdot 1 = 2

= \frac{- 1 + 3 i}{2}

Reescribir

\frac{- 1 + 3 i}{2}

en la forma binómica:

- \frac{1}{2} + \frac{3}{2} i

\frac{- 1 + 3 i}{2}

Aplicar las propiedades de las fracciones:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 1 + 3 i}{2} = - \frac{1}{2} + \frac{3 i}{2}

= - \frac{1}{2} + \frac{3 i}{2}

= - \frac{1}{2} + \frac{3}{2} i

u = \frac{- 1 - 3 i}{2 \cdot 1} : - \frac{1}{2} - i \frac{3}{2}

\frac{- 1 - 3 i}{2 \cdot 1}

Multiplicar los numeros:

2 \cdot 1 = 2

= \frac{- 1 - 3 i}{2}

Reescribir

\frac{- 1 - 3 i}{2}

en la forma binómica:

- \frac{1}{2} - \frac{3}{2} i

\frac{- 1 - 3 i}{2}

Aplicar las propiedades de las fracciones:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 1 - 3 i}{2} = - \frac{1}{2} - \frac{3 i}{2}

= - \frac{1}{2} - \frac{3 i}{2}

= - \frac{1}{2} - \frac{3}{2} i

Las soluciones a la ecuación de segundo grado son:

u = - \frac{1}{2} + i \frac{3}{2}, u = - \frac{1}{2} - i \frac{3}{2}

Sustituir en la ecuación

u = sin (x)

sin (x) = - \frac{1}{2} + i \frac{3}{2}, sin (x) = - \frac{1}{2} - i \frac{3}{2}

sin (x) = - \frac{1}{2} + i \frac{3}{2}, sin (x) = - \frac{1}{2} - i \frac{3}{2}

sin (x) = - \frac{1}{2} + i \frac{3}{2} :

Sin solución

sin (x) = - \frac{1}{2} + i \frac{3}{2}

Sin soluci \overset{o}{ˊ} n

sin (x) = - \frac{1}{2} - i \frac{3}{2} :

Sin solución

sin (x) = - \frac{1}{2} - i \frac{3}{2}

Sin soluci \overset{o}{ˊ} n

Combinar toda las soluciones

Sin soluci \overset{o}{ˊ} n

sec^{2} (x) + tan^{2} (x) - sec (x) tan (x) = 0 :

Sin solución

sec^{2} (x) + tan^{2} (x) - sec (x) tan (x) = 0

Expresar con seno, coseno

sec^{2} (x) + tan^{2} (x) - sec (x) tan (x)

Utilizar la identidad trigonométrica básica:

sec (x) = \frac{1}{cos ( x )}

= (\frac{1}{cos ( x )})^{2} + tan^{2} (x) - \frac{1}{cos ( x )} tan (x)

Utilizar la identidad trigonométrica básica:

tan (x) = \frac{sin ( x )}{cos ( x )}

= (\frac{1}{cos ( x )})^{2} + (\frac{sin ( x )}{cos ( x )})^{2} - \frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Simplificar

(\frac{1}{cos ( x )})^{2} + (\frac{sin ( x )}{cos ( x )})^{2} - \frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )} : \frac{1 + sin ^{2} ( x ) - sin ( x )}{cos ^{2} ( x )}

(\frac{1}{cos ( x )})^{2} + (\frac{sin ( x )}{cos ( x )})^{2} - \frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )}

(\frac{1}{cos ( x )})^{2} = \frac{1}{cos ^{2} ( x )}

(\frac{1}{cos ( x )})^{2}

Aplicar las leyes de los exponentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{cos ^{2} ( x )}

Aplicar la regla

1^{a} = 1

1^{2} = 1

= \frac{1}{cos ^{2} ( x )}

(\frac{sin ( x )}{cos ( x )})^{2} = \frac{sin ^{2} ( x )}{cos ^{2} ( x )}

(\frac{sin ( x )}{cos ( x )})^{2}

Aplicar las leyes de los exponentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{sin ^{2} ( x )}{cos ^{2} ( x )}

\frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )} = \frac{sin ( x )}{cos ^{2} ( x )}

\frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Multiplicar fracciones:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot sin ( x )}{cos ( x ) cos ( x )}

Multiplicar:

1 \cdot sin (x) = sin (x)

= \frac{sin ( x )}{cos ( x ) cos ( x )}

cos (x) cos (x) = cos^{2} (x)

cos (x) cos (x)

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

cos (x) cos (x) = cos^{1 + 1} (x)

= cos^{1 + 1} (x)

Sumar:

1 + 1 = 2

= cos^{2} (x)

= \frac{sin ( x )}{cos ^{2} ( x )}

= \frac{1}{cos ^{2} ( x )} + \frac{sin ^{2} ( x )}{cos ^{2} ( x )} - \frac{sin ( x )}{cos ^{2} ( x )}

Aplicar la regla

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{1 + sin ^{2} ( x ) - sin ( x )}{cos ^{2} ( x )}

= \frac{1 + sin ^{2} ( x ) - sin ( x )}{cos ^{2} ( x )}

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

1 - sin (x) + sin^{2} (x) = 0

Usando el método de sustitución

1 - sin (x) + sin^{2} (x) = 0

Sea:

sin (x) = u

1 - u + u^{2} = 0

1 - u + u^{2} = 0 : u = \frac{1}{2} + i \frac{3}{2}, u = \frac{1}{2} - i \frac{3}{2}

1 - u + u^{2} = 0

Escribir en la forma binómica

a x^{2} + b x + c = 0

u^{2} - u + 1 = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

u^{2} - u + 1 = 0

Formula general para ecuaciones de segundo grado:

Para

a = 1, b = - 1, c = 1

u_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 1 \cdot 1}{2 \cdot 1}

u_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 1 \cdot 1}{2 \cdot 1}

Simplificar

(- 1)^{2} - 4 \cdot 1 \cdot 1 : 3 i

(- 1)^{2} - 4 \cdot 1 \cdot 1

(- 1)^{2} = 1

(- 1)^{2}

Aplicar las leyes de los exponentes:

(- a)^{n} = a^{n},

n

es par

(- 1)^{2} = 1^{2}

= 1^{2}

Aplicar la regla

1^{a} = 1

= 1

4 \cdot 1 \cdot 1 = 4

4 \cdot 1 \cdot 1

Multiplicar los numeros:

4 \cdot 1 \cdot 1 = 4

= 4

= 1 - 4

Restar:

1 - 4 = - 3

= - 3

Aplicar las leyes de los exponentes:

- a = - 1 a

- 3 = - 1 3

= - 1 3

Aplicar las propiedades de los numeros imaginarios:

- 1 = i

= 3 i

u_{1, 2} = \frac{- ( - 1 ) \pm 3 i}{2 \cdot 1}

Separar las soluciones

u_{1} = \frac{- ( - 1 ) + 3 i}{2 \cdot 1}, u_{2} = \frac{- ( - 1 ) - 3 i}{2 \cdot 1}

u = \frac{- ( - 1 ) + 3 i}{2 \cdot 1} : \frac{1}{2} + i \frac{3}{2}

\frac{- ( - 1 ) + 3 i}{2 \cdot 1}

Aplicar la regla

- (- a) = a

= \frac{1 + 3 i}{2 \cdot 1}

Multiplicar los numeros:

2 \cdot 1 = 2

= \frac{1 + 3 i}{2}

Reescribir

\frac{1 + 3 i}{2}

en la forma binómica:

\frac{1}{2} + \frac{3}{2} i

\frac{1 + 3 i}{2}

Aplicar las propiedades de las fracciones:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{1 + 3 i}{2} = \frac{1}{2} + \frac{3 i}{2}

= \frac{1}{2} + \frac{3 i}{2}

= \frac{1}{2} + \frac{3}{2} i

u = \frac{- ( - 1 ) - 3 i}{2 \cdot 1} : \frac{1}{2} - i \frac{3}{2}

\frac{- ( - 1 ) - 3 i}{2 \cdot 1}

Aplicar la regla

- (- a) = a

= \frac{1 - 3 i}{2 \cdot 1}

Multiplicar los numeros:

2 \cdot 1 = 2

= \frac{1 - 3 i}{2}

Reescribir

\frac{1 - 3 i}{2}

en la forma binómica:

\frac{1}{2} - \frac{3}{2} i

\frac{1 - 3 i}{2}

Aplicar las propiedades de las fracciones:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{1 - 3 i}{2} = \frac{1}{2} - \frac{3 i}{2}

= \frac{1}{2} - \frac{3 i}{2}

= \frac{1}{2} - \frac{3}{2} i

Las soluciones a la ecuación de segundo grado son:

u = \frac{1}{2} + i \frac{3}{2}, u = \frac{1}{2} - i \frac{3}{2}

Sustituir en la ecuación

u = sin (x)

sin (x) = \frac{1}{2} + i \frac{3}{2}, sin (x) = \frac{1}{2} - i \frac{3}{2}

sin (x) = \frac{1}{2} + i \frac{3}{2}, sin (x) = \frac{1}{2} - i \frac{3}{2}

sin (x) = \frac{1}{2} + i \frac{3}{2} :

Sin solución

sin (x) = \frac{1}{2} + i \frac{3}{2}

Sin soluci \overset{o}{ˊ} n

sin (x) = \frac{1}{2} - i \frac{3}{2} :

Sin solución

sin (x) = \frac{1}{2} - i \frac{3}{2}

Sin soluci \overset{o}{ˊ} n

Combinar toda las soluciones

Sin soluci \overset{o}{ˊ} n

Combinar toda las soluciones

Sin soluci \overset{o}{ˊ} n para x \in R

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