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tan(x+32)=cot(x-20)

Solución

tan (x + 3 2^{\circ}) = cot (x - 2 0^{\circ})

Solución

x = 3 9^{\circ} + 18 0^{\circ} n, x = 12 9^{\circ} + 18 0^{\circ} n

radianes

x = \frac{13 π}{60} + πn, x = \frac{43 π}{60} + πn

Pasos de solución

tan (x + 3 2^{\circ}) = cot (x - 2 0^{\circ})

Restar

cot (x - 2 0^{\circ})

de ambos lados

tan (x + 3 2^{\circ}) - cot (x - 2 0^{\circ}) = 0

Simplificar

tan (x + 3 2^{\circ}) - cot (x - 2 0^{\circ}) : tan (\frac{45 x + 144 0 ^{\circ}}{45}) - cot (\frac{9 x - 18 0 ^{\circ}}{9})

tan (x + 3 2^{\circ}) - cot (x - 2 0^{\circ})

Simplificar

x + 3 2^{\circ}

en una fracción:

\frac{45 x + 144 0 ^{\circ}}{45}

x + 3 2^{\circ}

Convertir a fracción:

x = \frac{x 45}{45}

= \frac{x \cdot 45}{45} + 3 2^{\circ}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{x \cdot 45 + 144 0 ^{\circ}}{45}

= tan (\frac{45 x + 144 0 ^{\circ}}{45}) - cot (x - 2 0^{\circ})

Simplificar

x - 2 0^{\circ}

en una fracción:

\frac{9 x - 18 0 ^{\circ}}{9}

x - 2 0^{\circ}

Convertir a fracción:

x = \frac{x 9}{9}

= \frac{x \cdot 9}{9} - 2 0^{\circ}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{x \cdot 9 - 18 0 ^{\circ}}{9}

= tan (\frac{45 x + 144 0 ^{\circ}}{45}) - cot (\frac{9 x - 18 0 ^{\circ}}{9})

tan (\frac{45 x + 144 0 ^{\circ}}{45}) - cot (\frac{9 x - 18 0 ^{\circ}}{9}) = 0

Expresar con seno, coseno

- cot (\frac{- 18 0 ^{\circ} + 9 x}{9}) + tan (\frac{45 x + 144 0 ^{\circ}}{45})

Utilizar la identidad trigonométrica básica:

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

= - \frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} + tan (\frac{45 x + 144 0 ^{\circ}}{45})

Utilizar la identidad trigonométrica básica:

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

= - \frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} + \frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}

Simplificar

- \frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} + \frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} )} : \frac{- cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) + sin ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}{sin ( \frac{9 x - 18 0 ^{\circ}}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}

- \frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} + \frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}

Mínimo común múltiplo de

sin (\frac{- 18 0 ^{\circ} + 9 x}{9}), cos (\frac{45 x + 144 0 ^{\circ}}{45}) : sin (\frac{9 x - 18 0 ^{\circ}}{9}) cos (\frac{45 x + 144 0 ^{\circ}}{45})

sin (\frac{- 18 0 ^{\circ} + 9 x}{9}), cos (\frac{45 x + 144 0 ^{\circ}}{45})

Mínimo común múltiplo (MCM)

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

sin (\frac{- 18 0 ^{\circ} + 9 x}{9})

cos (\frac{45 x + 144 0 ^{\circ}}{45})

= sin (\frac{9 x - 18 0 ^{\circ}}{9}) cos (\frac{45 x + 144 0 ^{\circ}}{45})

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{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} :

multiplicar el denominador y el numerador por

cos (\frac{45 x + 144 0 ^{\circ}}{45})

\frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} = \frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}

Para

\frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} )} :

multiplicar el denominador y el numerador por

sin (\frac{9 x - 18 0 ^{\circ}}{9})

\frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} )} = \frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}

= - \frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )} + \frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{- cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) + sin ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}{sin ( \frac{9 x - 18 0 ^{\circ}}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}

= \frac{- cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) + sin ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}{sin ( \frac{9 x - 18 0 ^{\circ}}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}

\frac{- cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) + sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) sin ( \frac{45 x + 144 0 ^{\circ}}{45} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} = 0

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

- cos (\frac{- 18 0 ^{\circ} + 9 x}{9}) cos (\frac{45 x + 144 0 ^{\circ}}{45}) + sin (\frac{- 18 0 ^{\circ} + 9 x}{9}) sin (\frac{45 x + 144 0 ^{\circ}}{45}) = 0

Re-escribir usando identidades trigonométricas

- cos (\frac{- 18 0 ^{\circ} + 9 x}{9}) cos (\frac{45 x + 144 0 ^{\circ}}{45}) + sin (\frac{- 18 0 ^{\circ} + 9 x}{9}) sin (\frac{45 x + 144 0 ^{\circ}}{45})

Utilizar la identidad de suma de ángulos:

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

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

= - cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45})

- cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45}) = 0

Dividir ambos lados entre

- 1

- cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45}) = 0

Dividir ambos lados entre

- 1

\frac{- cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} )}{- 1} = \frac{0}{- 1}

Simplificar

cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45}) = 0

cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45}) = 0

Soluciones generales para

cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45}) = 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{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 9 0^{\circ} + 36 0^{\circ} n, \frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 27 0^{\circ} + 36 0^{\circ} n

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 9 0^{\circ} + 36 0^{\circ} n, \frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 27 0^{\circ} + 36 0^{\circ} n

Resolver

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 9 0^{\circ} + 36 0^{\circ} n : x = 3 9^{\circ} + 18 0^{\circ} n

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 9 0^{\circ} + 36 0^{\circ} n

Multiplicar por el mínimo común múltiplo

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 9 0^{\circ} + 36 0^{\circ} n

Encontrar el mínimo común múltiplo de

9, 45, 2 : 90

9, 45, 2

Mínimo común múltiplo (MCM)

Descomposición en factores primos de

9 : 3 \cdot 3

9

9

divida por

39 = 3 \cdot 3

= 3 \cdot 3

Descomposición en factores primos de

45 : 3 \cdot 3 \cdot 5

45

45

divida por

345 = 15 \cdot 3

= 3 \cdot 15

15

divida por

315 = 5 \cdot 3

= 3 \cdot 3 \cdot 5

3, 5

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

= 3 \cdot 3 \cdot 5

Descomposición en factores primos de

2 : 2

2

2

es un número primo, por lo tanto, no es posible factorizar

= 2

Calcular un número compuesto de factores que aparezcan al menos en alguno de los siguientes:

9, 45, 2

= 3 \cdot 3 \cdot 5 \cdot 2

Multiplicar los numeros:

3 \cdot 3 \cdot 5 \cdot 2 = 90

= 90

Multiplicar por el mínimo común múltiplo=

90

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90 + \frac{45 x + 144 0 ^{\circ}}{45} \cdot 90 = 9 0^{\circ} \cdot 90 + 36 0^{\circ} n \cdot 90

Simplificar

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90 + \frac{45 x + 144 0 ^{\circ}}{45} \cdot 90 = 9 0^{\circ} \cdot 90 + 36 0^{\circ} n \cdot 90

Simplificar

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90 : 10 (9 x - 18 0^{\circ})

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90

Multiplicar fracciones:

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

= \frac{( - 18 0 ^{\circ} + 9 x ) \cdot 90}{9}

Dividir:

\frac{90}{9} = 10

= 10 (9 x - 18 0^{\circ})

Simplificar

\frac{45 x + 144 0 ^{\circ}}{45} \cdot 90 : 2 (45 x + 144 0^{\circ})

\frac{45 x + 144 0 ^{\circ}}{45} \cdot 90

Multiplicar fracciones:

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

= \frac{( 45 x + 144 0 ^{\circ} ) \cdot 90}{45}

Dividir:

\frac{90}{45} = 2

= 2 (45 x + 144 0^{\circ})

Simplificar

9 0^{\circ} \cdot 90 : 810 0^{\circ}

9 0^{\circ} \cdot 90

Multiplicar fracciones:

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

= 810 0^{\circ}

Dividir:

\frac{90}{2} = 45

= 810 0^{\circ}

Simplificar

36 0^{\circ} n \cdot 90 : 3240 0^{\circ} n

36 0^{\circ} n \cdot 90

Multiplicar los numeros:

2 \cdot 90 = 180

= 3240 0^{\circ} n

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) = 810 0^{\circ} + 3240 0^{\circ} n

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) = 810 0^{\circ} + 3240 0^{\circ} n

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) = 810 0^{\circ} + 3240 0^{\circ} n

Desarrollar

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) : 180 x + 108 0^{\circ}

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ})

Expandir

10 (9 x - 18 0^{\circ}) : 90 x - 180 0^{\circ}

10 (9 x - 18 0^{\circ})

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 10, b = 9 x, c = 18 0^{\circ}

= 10 \cdot 9 x - 180 0^{\circ}

Multiplicar los numeros:

10 \cdot 9 = 90

= 90 x - 180 0^{\circ}

= 90 x - 180 0^{\circ} + 2 (45 x + 144 0^{\circ})

Expandir

2 (45 x + 144 0^{\circ}) : 90 x + 288 0^{\circ}

2 (45 x + 144 0^{\circ})

Poner los parentesis utilizando:

a (b + c) = ab + a c

a = 2, b = 45 x, c = 144 0^{\circ}

= 2 \cdot 45 x + 2 \cdot 144 0^{\circ}

Simplificar

2 \cdot 45 x + 2 \cdot 144 0^{\circ} : 90 x + 288 0^{\circ}

2 \cdot 45 x + 2 \cdot 144 0^{\circ}

Multiplicar los numeros:

2 \cdot 45 = 90

= 90 x + 2 \cdot 144 0^{\circ}

Multiplicar los numeros:

2 \cdot 8 = 16

= 90 x + 288 0^{\circ}

= 90 x + 288 0^{\circ}

= 90 x - 180 0^{\circ} + 90 x + 288 0^{\circ}

Simplificar

90 x - 180 0^{\circ} + 90 x + 288 0^{\circ} : 180 x + 108 0^{\circ}

90 x - 180 0^{\circ} + 90 x + 288 0^{\circ}

Agrupar términos semejantes

= 90 x + 90 x - 180 0^{\circ} + 288 0^{\circ}

Sumar elementos similares:

90 x + 90 x = 180 x

= 180 x - 180 0^{\circ} + 288 0^{\circ}

Sumar elementos similares:

- 180 0^{\circ} + 288 0^{\circ} = 108 0^{\circ}

= 180 x + 108 0^{\circ}

= 180 x + 108 0^{\circ}

180 x + 108 0^{\circ} = 810 0^{\circ} + 3240 0^{\circ} n

Mover

108 0^{\circ}

al lado derecho

180 x + 108 0^{\circ} = 810 0^{\circ} + 3240 0^{\circ} n

Restar

108 0^{\circ}

de ambos lados

180 x + 108 0^{\circ} - 108 0^{\circ} = 810 0^{\circ} + 3240 0^{\circ} n - 108 0^{\circ}

Simplificar

180 x = 702 0^{\circ} + 3240 0^{\circ} n

180 x = 702 0^{\circ} + 3240 0^{\circ} n

Dividir ambos lados entre

180

180 x = 702 0^{\circ} + 3240 0^{\circ} n

Dividir ambos lados entre

180

\frac{180 x}{180} = 3 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

Simplificar

\frac{180 x}{180} = 3 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

Simplificar

\frac{180 x}{180} : x

\frac{180 x}{180}

Dividir:

\frac{180}{180} = 1

= x

Simplificar

3 9^{\circ} + \frac{3240 0 ^{\circ} n}{180} : 3 9^{\circ} + 18 0^{\circ} n

3 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

Cancelar

3 9^{\circ} : 3 9^{\circ}

3 9^{\circ}

Eliminar los terminos comunes:

3

= 3 9^{\circ}

= 3 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

Dividir:

\frac{180}{180} = 1

= 3 9^{\circ} + 18 0^{\circ} n

x = 3 9^{\circ} + 18 0^{\circ} n

x = 3 9^{\circ} + 18 0^{\circ} n

x = 3 9^{\circ} + 18 0^{\circ} n

Resolver

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 27 0^{\circ} + 36 0^{\circ} n : x = 12 9^{\circ} + 18 0^{\circ} n

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 27 0^{\circ} + 36 0^{\circ} n

Multiplicar por el mínimo común múltiplo

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 27 0^{\circ} + 36 0^{\circ} n

Encontrar el mínimo común múltiplo de

9, 45, 2 : 90

9, 45, 2

Mínimo común múltiplo (MCM)

Descomposición en factores primos de

9 : 3 \cdot 3

9

9

divida por

39 = 3 \cdot 3

= 3 \cdot 3

Descomposición en factores primos de

45 : 3 \cdot 3 \cdot 5

45

45

divida por

345 = 15 \cdot 3

= 3 \cdot 15

15

divida por

315 = 5 \cdot 3

= 3 \cdot 3 \cdot 5

3, 5

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

= 3 \cdot 3 \cdot 5

Descomposición en factores primos de

2 : 2

2

2

es un número primo, por lo tanto, no es posible factorizar

= 2

Calcular un número compuesto de factores que aparezcan al menos en alguno de los siguientes:

9, 45, 2

= 3 \cdot 3 \cdot 5 \cdot 2

Multiplicar los numeros:

3 \cdot 3 \cdot 5 \cdot 2 = 90

= 90

Multiplicar por el mínimo común múltiplo=

90

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90 + \frac{45 x + 144 0 ^{\circ}}{45} \cdot 90 = 27 0^{\circ} \cdot 90 + 36 0^{\circ} n \cdot 90

Simplificar

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90 + \frac{45 x + 144 0 ^{\circ}}{45} \cdot 90 = 27 0^{\circ} \cdot 90 + 36 0^{\circ} n \cdot 90

Simplificar

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90 : 10 (9 x - 18 0^{\circ})

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90

Multiplicar fracciones:

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

= \frac{( - 18 0 ^{\circ} + 9 x ) \cdot 90}{9}

Dividir:

\frac{90}{9} = 10

= 10 (9 x - 18 0^{\circ})

Simplificar

\frac{45 x + 144 0 ^{\circ}}{45} \cdot 90 : 2 (45 x + 144 0^{\circ})

\frac{45 x + 144 0 ^{\circ}}{45} \cdot 90

Multiplicar fracciones:

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

= \frac{( 45 x + 144 0 ^{\circ} ) \cdot 90}{45}

Dividir:

\frac{90}{45} = 2

= 2 (45 x + 144 0^{\circ})

Simplificar

27 0^{\circ} \cdot 90 : 2430 0^{\circ}

27 0^{\circ} \cdot 90

Multiplicar fracciones:

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

= 2430 0^{\circ}

Multiplicar los numeros:

3 \cdot 90 = 270

= 2430 0^{\circ}

Dividir:

\frac{270}{2} = 135

= 2430 0^{\circ}

Simplificar

36 0^{\circ} n \cdot 90 : 3240 0^{\circ} n

36 0^{\circ} n \cdot 90

Multiplicar los numeros:

2 \cdot 90 = 180

= 3240 0^{\circ} n

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) = 2430 0^{\circ} + 3240 0^{\circ} n

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) = 2430 0^{\circ} + 3240 0^{\circ} n

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) = 2430 0^{\circ} + 3240 0^{\circ} n

Desarrollar

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) : 180 x + 108 0^{\circ}

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ})

Expandir

10 (9 x - 18 0^{\circ}) : 90 x - 180 0^{\circ}

10 (9 x - 18 0^{\circ})

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 10, b = 9 x, c = 18 0^{\circ}

= 10 \cdot 9 x - 180 0^{\circ}

Multiplicar los numeros:

10 \cdot 9 = 90

= 90 x - 180 0^{\circ}

= 90 x - 180 0^{\circ} + 2 (45 x + 144 0^{\circ})

Expandir

2 (45 x + 144 0^{\circ}) : 90 x + 288 0^{\circ}

2 (45 x + 144 0^{\circ})

Poner los parentesis utilizando:

a (b + c) = ab + a c

a = 2, b = 45 x, c = 144 0^{\circ}

= 2 \cdot 45 x + 2 \cdot 144 0^{\circ}

Simplificar

2 \cdot 45 x + 2 \cdot 144 0^{\circ} : 90 x + 288 0^{\circ}

2 \cdot 45 x + 2 \cdot 144 0^{\circ}

Multiplicar los numeros:

2 \cdot 45 = 90

= 90 x + 2 \cdot 144 0^{\circ}

Multiplicar los numeros:

2 \cdot 8 = 16

= 90 x + 288 0^{\circ}

= 90 x + 288 0^{\circ}

= 90 x - 180 0^{\circ} + 90 x + 288 0^{\circ}

Simplificar

90 x - 180 0^{\circ} + 90 x + 288 0^{\circ} : 180 x + 108 0^{\circ}

90 x - 180 0^{\circ} + 90 x + 288 0^{\circ}

Agrupar términos semejantes

= 90 x + 90 x - 180 0^{\circ} + 288 0^{\circ}

Sumar elementos similares:

90 x + 90 x = 180 x

= 180 x - 180 0^{\circ} + 288 0^{\circ}

Sumar elementos similares:

- 180 0^{\circ} + 288 0^{\circ} = 108 0^{\circ}

= 180 x + 108 0^{\circ}

= 180 x + 108 0^{\circ}

180 x + 108 0^{\circ} = 2430 0^{\circ} + 3240 0^{\circ} n

Mover

108 0^{\circ}

al lado derecho

180 x + 108 0^{\circ} = 2430 0^{\circ} + 3240 0^{\circ} n

Restar

108 0^{\circ}

de ambos lados

180 x + 108 0^{\circ} - 108 0^{\circ} = 2430 0^{\circ} + 3240 0^{\circ} n - 108 0^{\circ}

Simplificar

180 x = 2322 0^{\circ} + 3240 0^{\circ} n

180 x = 2322 0^{\circ} + 3240 0^{\circ} n

Dividir ambos lados entre

180

180 x = 2322 0^{\circ} + 3240 0^{\circ} n

Dividir ambos lados entre

180

\frac{180 x}{180} = 12 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

Simplificar

\frac{180 x}{180} = 12 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

Simplificar

\frac{180 x}{180} : x

\frac{180 x}{180}

Dividir:

\frac{180}{180} = 1

= x

Simplificar

12 9^{\circ} + \frac{3240 0 ^{\circ} n}{180} : 12 9^{\circ} + 18 0^{\circ} n

12 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

Cancelar

12 9^{\circ} : 12 9^{\circ}

12 9^{\circ}

Eliminar los terminos comunes:

3

= 12 9^{\circ}

= 12 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

Dividir:

\frac{180}{180} = 1

= 12 9^{\circ} + 18 0^{\circ} n

x = 12 9^{\circ} + 18 0^{\circ} n

x = 12 9^{\circ} + 18 0^{\circ} n

x = 12 9^{\circ} + 18 0^{\circ} n

x = 3 9^{\circ} + 18 0^{\circ} n, x = 12 9^{\circ} + 18 0^{\circ} n

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17 cos (x) + 9 = - cos (x)

(2cos(θ)+1)(cos(θ)-2)=0

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