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sin(90-2x)=cos(90-x)

Solución

sin (90 - 2 x) = cos (9 0^{\circ} - x)

Solución

x = - 18 0^{\circ} + 90 - 72 0^{\circ} n, x = - 54 0^{\circ} + 90 - 72 0^{\circ} n, x = - \frac{72 0 ^{\circ} n}{3} + 30, x = - 12 0^{\circ} + 30 - \frac{72 0 ^{\circ} n}{3}

radianes

x = - π + 90 - 4 πn, x = - 3 π + 90 - 4 πn, x = 30 - \frac{4 π}{3} n, x = - \frac{2 π}{3} + 30 - \frac{4 π}{3} n

Pasos de solución

sin (90 - 2 x) = cos (9 0^{\circ} - x)

Re-escribir usando identidades trigonométricas

sin (90 - 2 x) = cos (9 0^{\circ} - x)

Re-escribir usando identidades trigonométricas

cos (9 0^{\circ} - x)

Utilizar la identidad de diferencia de ángulos:

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

= cos (9 0^{\circ}) cos (x) + sin (9 0^{\circ}) sin (x)

Simplificar

cos (9 0^{\circ}) cos (x) + sin (9 0^{\circ}) sin (x) : sin (x)

cos (9 0^{\circ}) cos (x) + sin (9 0^{\circ}) sin (x)

cos (9 0^{\circ}) cos (x) = 0

cos (9 0^{\circ}) cos (x)

Simplificar

cos (9 0^{\circ}) : 0

cos (9 0^{\circ})

Utilizar la siguiente identidad trivial:

cos (9 0^{\circ}) = 0

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0 \cdot cos (x)

Aplicar la regla

0 \cdot a = 0

= 0

sin (9 0^{\circ}) sin (x) = sin (x)

sin (9 0^{\circ}) sin (x)

Simplificar

sin (9 0^{\circ}) : 1

sin (9 0^{\circ})

Utilizar la siguiente identidad trivial:

sin (9 0^{\circ}) = 1

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1 \cdot sin (x)

Multiplicar:

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

= sin (x)

= 0 + sin (x)

0 + sin (x) = sin (x)

= sin (x)

= sin (x)

sin (90 - 2 x) = sin (x)

sin (90 - 2 x) = sin (x)

Restar

sin (x)

de ambos lados

sin (90 - 2 x) - sin (x) = 0

Re-escribir usando identidades trigonométricas

sin (90 - 2 x) - sin (x)

Utilizar la identidad suma-producto:

sin (s) - sin (t) = 2 sin (\frac{s - t}{2}) cos (\frac{s + t}{2})

= 2 sin (\frac{90 - 2 x - x}{2}) cos (\frac{90 - 2 x + x}{2})

Simplificar

2 sin (\frac{90 - 2 x - x}{2}) cos (\frac{90 - 2 x + x}{2}) : 2 sin (\frac{90 - 3 x}{2}) cos (\frac{90 - x}{2})

2 sin (\frac{90 - 2 x - x}{2}) cos (\frac{90 - 2 x + x}{2})

Sumar elementos similares:

- 2 x - x = - 3 x

= 2 sin (\frac{- 3 x + 90}{2}) cos (\frac{x - 2 x + 90}{2})

Sumar elementos similares:

- 2 x + x = - x

= 2 sin (\frac{- 3 x + 90}{2}) cos (\frac{- x + 90}{2})

= 2 sin (\frac{90 - 3 x}{2}) cos (\frac{90 - x}{2})

2 cos (\frac{90 - x}{2}) sin (\frac{90 - 3 x}{2}) = 0

Resolver cada parte por separado

cos (\frac{90 - x}{2}) = 0 or sin (\frac{90 - 3 x}{2}) = 0

cos (\frac{90 - x}{2}) = 0 : x = - 18 0^{\circ} + 90 - 72 0^{\circ} n, x = - 54 0^{\circ} + 90 - 72 0^{\circ} n

cos (\frac{90 - x}{2}) = 0

Soluciones generales para

cos (\frac{90 - x}{2}) = 0

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

\frac{90 - x}{2} = 9 0^{\circ} + 36 0^{\circ} n, \frac{90 - x}{2} = 27 0^{\circ} + 36 0^{\circ} n

\frac{90 - x}{2} = 9 0^{\circ} + 36 0^{\circ} n, \frac{90 - x}{2} = 27 0^{\circ} + 36 0^{\circ} n

Resolver

\frac{90 - x}{2} = 9 0^{\circ} + 36 0^{\circ} n : x = - 18 0^{\circ} + 90 - 72 0^{\circ} n

\frac{90 - x}{2} = 9 0^{\circ} + 36 0^{\circ} n

Multiplicar ambos lados por

2

\frac{90 - x}{2} = 9 0^{\circ} + 36 0^{\circ} n

Multiplicar ambos lados por

2

\frac{2 ( 90 - x )}{2} = 2 \cdot 9 0^{\circ} + 2 \cdot 36 0^{\circ} n

Simplificar

\frac{2 ( 90 - x )}{2} = 2 \cdot 9 0^{\circ} + 2 \cdot 36 0^{\circ} n

Simplificar

\frac{2 ( 90 - x )}{2} : 90 - x

\frac{2 ( 90 - x )}{2}

Dividir:

\frac{2}{2} = 1

= 90 - x

Simplificar

2 \cdot 9 0^{\circ} + 2 \cdot 36 0^{\circ} n : 18 0^{\circ} + 72 0^{\circ} n

2 \cdot 9 0^{\circ} + 2 \cdot 36 0^{\circ} n

2 \cdot 9 0^{\circ} = 18 0^{\circ}

2 \cdot 9 0^{\circ}

Multiplicar fracciones:

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

= 18 0^{\circ}

Eliminar los terminos comunes:

2

= 18 0^{\circ}

2 \cdot 36 0^{\circ} n = 72 0^{\circ} n

2 \cdot 36 0^{\circ} n

Multiplicar los numeros:

2 \cdot 2 = 4

= 72 0^{\circ} n

= 18 0^{\circ} + 72 0^{\circ} n

90 - x = 18 0^{\circ} + 72 0^{\circ} n

90 - x = 18 0^{\circ} + 72 0^{\circ} n

90 - x = 18 0^{\circ} + 72 0^{\circ} n

Mover

90

al lado derecho

90 - x = 18 0^{\circ} + 72 0^{\circ} n

Restar

90

de ambos lados

90 - x - 90 = 18 0^{\circ} + 72 0^{\circ} n - 90

Simplificar

- x = 18 0^{\circ} + 72 0^{\circ} n - 90

- x = 18 0^{\circ} + 72 0^{\circ} n - 90

Dividir ambos lados entre

- 1

- x = 18 0^{\circ} + 72 0^{\circ} n - 90

Dividir ambos lados entre

- 1

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{90}{- 1}

Simplificar

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{90}{- 1}

Simplificar

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

Aplicar la regla

\frac{a}{1} = a

= x

Simplificar

\frac{18 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{90}{- 1} : - 18 0^{\circ} + 90 - 72 0^{\circ} n

\frac{18 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{90}{- 1}

Agrupar términos semejantes

= \frac{18 0 ^{\circ}}{- 1} - \frac{90}{- 1} + \frac{72 0 ^{\circ} n}{- 1}

\frac{18 0 ^{\circ}}{- 1} = - 18 0^{\circ}

\frac{18 0 ^{\circ}}{- 1}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - 18 0^{\circ}

Aplicar la regla

\frac{a}{1} = a

= - 18 0^{\circ}

= - 18 0^{\circ} - \frac{90}{- 1} + \frac{72 0 ^{\circ} n}{- 1}

\frac{90}{- 1} = - 90

\frac{90}{- 1}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{90}{1}

Aplicar la regla

\frac{a}{1} = a

= - 90

\frac{72 0 ^{\circ} n}{- 1} = - 72 0^{\circ} n

\frac{72 0 ^{\circ} n}{- 1}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{72 0 ^{\circ} n}{1}

Aplicar la regla

\frac{a}{1} = a

= - 72 0^{\circ} n

= - 18 0^{\circ} - (- 90) - 72 0^{\circ} n

Aplicar la regla

- (- a) = a

= - 18 0^{\circ} + 90 - 72 0^{\circ} n

x = - 18 0^{\circ} + 90 - 72 0^{\circ} n

x = - 18 0^{\circ} + 90 - 72 0^{\circ} n

x = - 18 0^{\circ} + 90 - 72 0^{\circ} n

Resolver

\frac{90 - x}{2} = 27 0^{\circ} + 36 0^{\circ} n : x = - 54 0^{\circ} + 90 - 72 0^{\circ} n

\frac{90 - x}{2} = 27 0^{\circ} + 36 0^{\circ} n

Multiplicar ambos lados por

2

\frac{90 - x}{2} = 27 0^{\circ} + 36 0^{\circ} n

Multiplicar ambos lados por

2

\frac{2 ( 90 - x )}{2} = 2 \cdot 27 0^{\circ} + 2 \cdot 36 0^{\circ} n

Simplificar

\frac{2 ( 90 - x )}{2} = 2 \cdot 27 0^{\circ} + 2 \cdot 36 0^{\circ} n

Simplificar

\frac{2 ( 90 - x )}{2} : 90 - x

\frac{2 ( 90 - x )}{2}

Dividir:

\frac{2}{2} = 1

= 90 - x

Simplificar

2 \cdot 27 0^{\circ} + 2 \cdot 36 0^{\circ} n : 54 0^{\circ} + 72 0^{\circ} n

2 \cdot 27 0^{\circ} + 2 \cdot 36 0^{\circ} n

2 \cdot 27 0^{\circ} = 54 0^{\circ}

2 \cdot 27 0^{\circ}

Multiplicar fracciones:

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

= 54 0^{\circ}

Eliminar los terminos comunes:

2

= 54 0^{\circ}

2 \cdot 36 0^{\circ} n = 72 0^{\circ} n

2 \cdot 36 0^{\circ} n

Multiplicar los numeros:

2 \cdot 2 = 4

= 72 0^{\circ} n

= 54 0^{\circ} + 72 0^{\circ} n

90 - x = 54 0^{\circ} + 72 0^{\circ} n

90 - x = 54 0^{\circ} + 72 0^{\circ} n

90 - x = 54 0^{\circ} + 72 0^{\circ} n

Mover

90

al lado derecho

90 - x = 54 0^{\circ} + 72 0^{\circ} n

Restar

90

de ambos lados

90 - x - 90 = 54 0^{\circ} + 72 0^{\circ} n - 90

Simplificar

- x = 54 0^{\circ} + 72 0^{\circ} n - 90

- x = 54 0^{\circ} + 72 0^{\circ} n - 90

Dividir ambos lados entre

- 1

- x = 54 0^{\circ} + 72 0^{\circ} n - 90

Dividir ambos lados entre

- 1

\frac{- x}{- 1} = \frac{54 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{90}{- 1}

Simplificar

\frac{- x}{- 1} = \frac{54 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{90}{- 1}

Simplificar

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

Aplicar la regla

\frac{a}{1} = a

= x

Simplificar

\frac{54 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{90}{- 1} : - 54 0^{\circ} + 90 - 72 0^{\circ} n

\frac{54 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{90}{- 1}

Agrupar términos semejantes

= \frac{54 0 ^{\circ}}{- 1} - \frac{90}{- 1} + \frac{72 0 ^{\circ} n}{- 1}

\frac{54 0 ^{\circ}}{- 1} = - 54 0^{\circ}

\frac{54 0 ^{\circ}}{- 1}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - 54 0^{\circ}

Aplicar la regla

\frac{a}{1} = a

= - 54 0^{\circ}

= - 54 0^{\circ} - \frac{90}{- 1} + \frac{72 0 ^{\circ} n}{- 1}

\frac{90}{- 1} = - 90

\frac{90}{- 1}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{90}{1}

Aplicar la regla

\frac{a}{1} = a

= - 90

\frac{72 0 ^{\circ} n}{- 1} = - 72 0^{\circ} n

\frac{72 0 ^{\circ} n}{- 1}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{72 0 ^{\circ} n}{1}

Aplicar la regla

\frac{a}{1} = a

= - 72 0^{\circ} n

= - 54 0^{\circ} - (- 90) - 72 0^{\circ} n

Aplicar la regla

- (- a) = a

= - 54 0^{\circ} + 90 - 72 0^{\circ} n

x = - 54 0^{\circ} + 90 - 72 0^{\circ} n

x = - 54 0^{\circ} + 90 - 72 0^{\circ} n

x = - 54 0^{\circ} + 90 - 72 0^{\circ} n

x = - 18 0^{\circ} + 90 - 72 0^{\circ} n, x = - 54 0^{\circ} + 90 - 72 0^{\circ} n

sin (\frac{90 - 3 x}{2}) = 0 : x = - \frac{72 0 ^{\circ} n}{3} + 30, x = - 12 0^{\circ} + 30 - \frac{72 0 ^{\circ} n}{3}

sin (\frac{90 - 3 x}{2}) = 0

Soluciones generales para

sin (\frac{90 - 3 x}{2}) = 0

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{90 - 3 x}{2} = 0 + 36 0^{\circ} n, \frac{90 - 3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n

\frac{90 - 3 x}{2} = 0 + 36 0^{\circ} n, \frac{90 - 3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n

Resolver

\frac{90 - 3 x}{2} = 0 + 36 0^{\circ} n : x = - \frac{72 0 ^{\circ} n}{3} + 30

\frac{90 - 3 x}{2} = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

\frac{90 - 3 x}{2} = 36 0^{\circ} n

Multiplicar ambos lados por

2

\frac{90 - 3 x}{2} = 36 0^{\circ} n

Multiplicar ambos lados por

2

\frac{2 ( 90 - 3 x )}{2} = 2 \cdot 36 0^{\circ} n

Simplificar

90 - 3 x = 72 0^{\circ} n

90 - 3 x = 72 0^{\circ} n

Mover

90

al lado derecho

90 - 3 x = 72 0^{\circ} n

Restar

90

de ambos lados

90 - 3 x - 90 = 72 0^{\circ} n - 90

Simplificar

- 3 x = 72 0^{\circ} n - 90

- 3 x = 72 0^{\circ} n - 90

Dividir ambos lados entre

- 3

- 3 x = 72 0^{\circ} n - 90

Dividir ambos lados entre

- 3

\frac{- 3 x}{- 3} = \frac{72 0 ^{\circ} n}{- 3} - \frac{90}{- 3}

Simplificar

\frac{- 3 x}{- 3} = \frac{72 0 ^{\circ} n}{- 3} - \frac{90}{- 3}

Simplificar

\frac{- 3 x}{- 3} : x

\frac{- 3 x}{- 3}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

\frac{72 0 ^{\circ} n}{- 3} - \frac{90}{- 3} : - \frac{72 0 ^{\circ} n}{3} + 30

\frac{72 0 ^{\circ} n}{- 3} - \frac{90}{- 3}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{72 0 ^{\circ} n}{3} - \frac{90}{- 3}

\frac{90}{- 3} = - 30

\frac{90}{- 3}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{90}{3}

Dividir:

\frac{90}{3} = 30

= - 30

= - \frac{72 0 ^{\circ} n}{3} - (- 30)

Aplicar la regla

- (- a) = a

= - \frac{72 0 ^{\circ} n}{3} + 30

x = - \frac{72 0 ^{\circ} n}{3} + 30

x = - \frac{72 0 ^{\circ} n}{3} + 30

x = - \frac{72 0 ^{\circ} n}{3} + 30

Resolver

\frac{90 - 3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n : x = - 12 0^{\circ} + 30 - \frac{72 0 ^{\circ} n}{3}

\frac{90 - 3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n

Multiplicar ambos lados por

2

\frac{90 - 3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n

Multiplicar ambos lados por

2

\frac{2 ( 90 - 3 x )}{2} = 36 0^{\circ} + 2 \cdot 36 0^{\circ} n

Simplificar

90 - 3 x = 36 0^{\circ} + 72 0^{\circ} n

90 - 3 x = 36 0^{\circ} + 72 0^{\circ} n

Mover

90

al lado derecho

90 - 3 x = 36 0^{\circ} + 72 0^{\circ} n

Restar

90

de ambos lados

90 - 3 x - 90 = 36 0^{\circ} + 72 0^{\circ} n - 90

Simplificar

- 3 x = 36 0^{\circ} + 72 0^{\circ} n - 90

- 3 x = 36 0^{\circ} + 72 0^{\circ} n - 90

Dividir ambos lados entre

- 3

- 3 x = 36 0^{\circ} + 72 0^{\circ} n - 90

Dividir ambos lados entre

- 3

\frac{- 3 x}{- 3} = \frac{36 0 ^{\circ}}{- 3} + \frac{72 0 ^{\circ} n}{- 3} - \frac{90}{- 3}

Simplificar

\frac{- 3 x}{- 3} = \frac{36 0 ^{\circ}}{- 3} + \frac{72 0 ^{\circ} n}{- 3} - \frac{90}{- 3}

Simplificar

\frac{- 3 x}{- 3} : x

\frac{- 3 x}{- 3}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

\frac{36 0 ^{\circ}}{- 3} + \frac{72 0 ^{\circ} n}{- 3} - \frac{90}{- 3} : - 12 0^{\circ} + 30 - \frac{72 0 ^{\circ} n}{3}

\frac{36 0 ^{\circ}}{- 3} + \frac{72 0 ^{\circ} n}{- 3} - \frac{90}{- 3}

Agrupar términos semejantes

= \frac{36 0 ^{\circ}}{- 3} - \frac{90}{- 3} + \frac{72 0 ^{\circ} n}{- 3}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - 12 0^{\circ} - \frac{90}{- 3} + \frac{72 0 ^{\circ} n}{- 3}

\frac{90}{- 3} = - 30

\frac{90}{- 3}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{90}{3}

Dividir:

\frac{90}{3} = 30

= - 30

\frac{72 0 ^{\circ} n}{- 3} = - \frac{72 0 ^{\circ} n}{3}

\frac{72 0 ^{\circ} n}{- 3}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{72 0 ^{\circ} n}{3}

= - 12 0^{\circ} - (- 30) - \frac{72 0 ^{\circ} n}{3}

Aplicar la regla

- (- a) = a

= - 12 0^{\circ} + 30 - \frac{72 0 ^{\circ} n}{3}

x = - 12 0^{\circ} + 30 - \frac{72 0 ^{\circ} n}{3}

x = - 12 0^{\circ} + 30 - \frac{72 0 ^{\circ} n}{3}

x = - 12 0^{\circ} + 30 - \frac{72 0 ^{\circ} n}{3}

x = - \frac{72 0 ^{\circ} n}{3} + 30, x = - 12 0^{\circ} + 30 - \frac{72 0 ^{\circ} n}{3}

Combinar toda las soluciones

x = - 18 0^{\circ} + 90 - 72 0^{\circ} n, x = - 54 0^{\circ} + 90 - 72 0^{\circ} n, x = - \frac{72 0 ^{\circ} n}{3} + 30, x = - 12 0^{\circ} + 30 - \frac{72 0 ^{\circ} n}{3}

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