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Popular Trigonometría >

arccos(2x)+arccos(x)= pi/3

Solución

arccos (2 x) + arccos (x) = \frac{π}{3}

Solución

x = \frac{1}{2}

Pasos de solución

arccos (2 x) + arccos (x) = \frac{π}{3}

Re-escribir usando identidades trigonométricas

arccos (2 x) + arccos (x)

Utilizar la identidad suma-producto:

arccos (s) + arccos (t) = arccos (s t - (1 - s^{2}) (1 - t^{2}))

= arccos (2 xx - (1 - (2 x)^{2}) (1 - x^{2}))

arccos (2 xx - (1 - (2 x)^{2}) (1 - x^{2})) = \frac{π}{3}

Aplicar propiedades trigonométricas inversas

arccos (2 xx - (1 - (2 x)^{2}) (1 - x^{2})) = \frac{π}{3}

arccos (x) = a \Rightarrow x = cos (a)

2 xx - (1 - (2 x)^{2}) (1 - x^{2}) = cos (\frac{π}{3})

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

Utilizar la siguiente identidad trivial:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

cos (x)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

= \frac{1}{2}

2 xx - (1 - (2 x)^{2}) (1 - x^{2}) = \frac{1}{2}

2 xx - (1 - (2 x)^{2}) (1 - x^{2}) = \frac{1}{2}

Resolver

2 xx - (1 - (2 x)^{2}) (1 - x^{2}) = \frac{1}{2} : x = \frac{1}{2}, x = - \frac{1}{2}

2 xx - (1 - (2 x)^{2}) (1 - x^{2}) = \frac{1}{2}

Multiplicar ambos lados por

2

2 xx \cdot 2 - (1 - (2 x)^{2}) (1 - x^{2}) \cdot 2 = \frac{1}{2} \cdot 2

Simplificar

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

Eliminar raíces cuadradas

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

Restar

4 x^{2}

de ambos lados

4 x^{2} - 2 (1 - (2 x)^{2}) (1 - x^{2}) - 4 x^{2} = 1 - 4 x^{2}

Simplificar

- 2 (1 - (2 x)^{2}) (1 - x^{2}) = 1 - 4 x^{2}

Elevar al cuadrado ambos lados:

4 - 20 x^{2} + 16 x^{4} = 1 - 8 x^{2} + 16 x^{4}

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

(- 2 (1 - (2 x)^{2}) (1 - x^{2}))^{2} = (1 - 4 x^{2})^{2}

Desarrollar

(- 2 (1 - (2 x)^{2}) (1 - x^{2}))^{2} : 4 - 20 x^{2} + 16 x^{4}

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

Aplicar las leyes de los exponentes:

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

n

es par

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

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

Aplicar las leyes de los exponentes:

(a \cdot b)^{n} = a^{n} b^{n}

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

((1 - (2 x)^{2}) (1 - x^{2}))^{2} : (1 - (2 x)^{2}) (1 - x^{2})

Aplicar las leyes de los exponentes:

a = a^{\frac{1}{2}}

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

Aplicar las leyes de los exponentes:

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

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

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiplicar fracciones:

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

= \frac{1 \cdot 2}{2}

Eliminar los terminos comunes:

2

= 1

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

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

2^{2} = 4

= 4 (1 - (2 x)^{2}) (1 - x^{2})

Desarrollar

4 (1 - (2 x)^{2}) (1 - x^{2}) : 4 - 20 x^{2} + 16 x^{4}

4 (1 - (2 x)^{2}) (1 - x^{2})

Aplicar las leyes de los exponentes:

(a \cdot b)^{n} = a^{n} b^{n}

= 4 (- 2^{2} x^{2} + 1) (- x^{2} + 1)

2^{2} = 4

= 4 (- 4 x^{2} + 1) (- x^{2} + 1)

Expandir

(1 - 4 x^{2}) (1 - x^{2}) : 1 - 5 x^{2} + 4 x^{4}

(1 - 4 x^{2}) (1 - x^{2})

Aplicar la propiedad distributiva:

(a + b) (c + d) = a c + a d + b c + b d

a = 1, b = - 4 x^{2}, c = 1, d = - x^{2}

= 1 \cdot 1 + 1 \cdot (- x^{2}) + (- 4 x^{2}) \cdot 1 + (- 4 x^{2}) (- x^{2})

Aplicar las reglas de los signos

+ (- a) = - a, (- a) (- b) = ab

= 1 \cdot 1 - 1 \cdot x^{2} - 4 \cdot 1 \cdot x^{2} + 4 x^{2} x^{2}

Simplificar

1 \cdot 1 - 1 \cdot x^{2} - 4 \cdot 1 \cdot x^{2} + 4 x^{2} x^{2} : 1 - 5 x^{2} + 4 x^{4}

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

1 \cdot 1 = 1

1 \cdot 1

Multiplicar los numeros:

1 \cdot 1 = 1

= 1

1 \cdot x^{2} = x^{2}

1 \cdot x^{2}

Multiplicar:

1 \cdot x^{2} = x^{2}

= x^{2}

4 \cdot 1 \cdot x^{2} = 4 x^{2}

4 \cdot 1 \cdot x^{2}

Multiplicar los numeros:

4 \cdot 1 = 4

= 4 x^{2}

4 x^{2} x^{2} = 4 x^{4}

4 x^{2} x^{2}

Aplicar las leyes de los exponentes:

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

x^{2} x^{2} = x^{2 + 2}

= 4 x^{2 + 2}

Sumar:

2 + 2 = 4

= 4 x^{4}

= 1 - x^{2} - 4 x^{2} + 4 x^{4}

Sumar elementos similares:

- x^{2} - 4 x^{2} = - 5 x^{2}

= 1 - 5 x^{2} + 4 x^{4}

= 1 - 5 x^{2} + 4 x^{4}

= 4 (1 - 5 x^{2} + 4 x^{4})

Expandir

4 (1 - 5 x^{2} + 4 x^{4}) : 4 - 20 x^{2} + 16 x^{4}

4 (1 - 5 x^{2} + 4 x^{4})

Aplicar la siguiente regla de productos notables

= 4 \cdot 1 + 4 (- 5 x^{2}) + 4 \cdot 4 x^{4}

Aplicar las reglas de los signos

+ (- a) = - a

= 4 \cdot 1 - 4 \cdot 5 x^{2} + 4 \cdot 4 x^{4}

Simplificar

4 \cdot 1 - 4 \cdot 5 x^{2} + 4 \cdot 4 x^{4} : 4 - 20 x^{2} + 16 x^{4}

4 \cdot 1 - 4 \cdot 5 x^{2} + 4 \cdot 4 x^{4}

Multiplicar los numeros:

4 \cdot 1 = 4

= 4 - 4 \cdot 5 x^{2} + 4 \cdot 4 x^{4}

Multiplicar los numeros:

4 \cdot 5 = 20

= 4 - 20 x^{2} + 4 \cdot 4 x^{4}

Multiplicar los numeros:

4 \cdot 4 = 16

= 4 - 20 x^{2} + 16 x^{4}

= 4 - 20 x^{2} + 16 x^{4}

= 4 - 20 x^{2} + 16 x^{4}

= 4 - 20 x^{2} + 16 x^{4}

Desarrollar

(1 - 4 x^{2})^{2} : 1 - 8 x^{2} + 16 x^{4}

(1 - 4 x^{2})^{2}

Aplicar la formula del binomio al cuadrado:

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

a = 1, b = 4 x^{2}

= 1^{2} - 2 \cdot 1 \cdot 4 x^{2} + (4 x^{2})^{2}

Simplificar

1^{2} - 2 \cdot 1 \cdot 4 x^{2} + (4 x^{2})^{2} : 1 - 8 x^{2} + 16 x^{4}

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

Aplicar la regla

1^{a} = 1

1^{2} = 1

= 1 - 2 \cdot 1 \cdot 4 x^{2} + (4 x^{2})^{2}

2 \cdot 1 \cdot 4 x^{2} = 8 x^{2}

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

Multiplicar los numeros:

2 \cdot 1 \cdot 4 = 8

= 8 x^{2}

(4 x^{2})^{2} = 16 x^{4}

(4 x^{2})^{2}

Aplicar las leyes de los exponentes:

(a \cdot b)^{n} = a^{n} b^{n}

= 4^{2} (x^{2})^{2}

(x^{2})^{2} : x^{4}

Aplicar las leyes de los exponentes:

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

= x^{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= x^{4}

= 4^{2} x^{4}

4^{2} = 16

= 16 x^{4}

= 1 - 8 x^{2} + 16 x^{4}

= 1 - 8 x^{2} + 16 x^{4}

4 - 20 x^{2} + 16 x^{4} = 1 - 8 x^{2} + 16 x^{4}

4 - 20 x^{2} + 16 x^{4} = 1 - 8 x^{2} + 16 x^{4}

4 - 20 x^{2} + 16 x^{4} = 1 - 8 x^{2} + 16 x^{4}

Resolver

4 - 20 x^{2} + 16 x^{4} = 1 - 8 x^{2} + 16 x^{4} : x = \frac{1}{2}, x = - \frac{1}{2}

4 - 20 x^{2} + 16 x^{4} = 1 - 8 x^{2} + 16 x^{4}

Desplace

4

a la derecha

4 - 20 x^{2} + 16 x^{4} = 1 - 8 x^{2} + 16 x^{4}

Restar

4

de ambos lados

4 - 20 x^{2} + 16 x^{4} - 4 = 1 - 8 x^{2} + 16 x^{4} - 4

Simplificar

- 20 x^{2} + 16 x^{4} = 16 x^{4} - 8 x^{2} - 3

- 20 x^{2} + 16 x^{4} = 16 x^{4} - 8 x^{2} - 3

Desplace

8 x^{2}

a la izquierda

- 20 x^{2} + 16 x^{4} = 16 x^{4} - 8 x^{2} - 3

Sumar

8 x^{2}

a ambos lados

- 20 x^{2} + 16 x^{4} + 8 x^{2} = 16 x^{4} - 8 x^{2} - 3 + 8 x^{2}

Simplificar

16 x^{4} - 12 x^{2} = 16 x^{4} - 3

16 x^{4} - 12 x^{2} = 16 x^{4} - 3

Desplace

16 x^{4}

a la izquierda

16 x^{4} - 12 x^{2} = 16 x^{4} - 3

Restar

16 x^{4}

de ambos lados

16 x^{4} - 12 x^{2} - 16 x^{4} = 16 x^{4} - 3 - 16 x^{4}

Simplificar

- 12 x^{2} = - 3

- 12 x^{2} = - 3

Dividir ambos lados entre

- 12

- 12 x^{2} = - 3

Dividir ambos lados entre

- 12

\frac{- 12 x ^{2}}{- 12} = \frac{- 3}{- 12}

Simplificar

\frac{- 12 x ^{2}}{- 12} = \frac{- 3}{- 12}

Simplificar

\frac{- 12 x ^{2}}{- 12} : x^{2}

\frac{- 12 x ^{2}}{- 12}

Aplicar las propiedades de las fracciones:

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

= \frac{12 x ^{2}}{12}

Dividir:

\frac{12}{12} = 1

= x^{2}

Simplificar

\frac{- 3}{- 12} : \frac{1}{4}

\frac{- 3}{- 12}

Aplicar las propiedades de las fracciones:

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

= \frac{3}{12}

Eliminar los terminos comunes:

3

= \frac{1}{4}

x^{2} = \frac{1}{4}

x^{2} = \frac{1}{4}

x^{2} = \frac{1}{4}

Para

x^{2} = f (a)

las soluciones son

x = f (a), - f (a)

x = \frac{1}{4}, x = - \frac{1}{4}

\frac{1}{4} = \frac{1}{2}

\frac{1}{4}

Aplicar las leyes de los exponentes:

\frac{a}{b} = \frac{a}{b}, a \geq 0, b \geq 0

= \frac{1}{4}

Aplicar las leyes de los exponentes:

1 = 1

1 = 1

= \frac{1}{4}

4 = 2

4

Descomponer el número en factores primos:

4 = 2^{2}

= 2^{2}

Aplicar las leyes de los exponentes:

a^{2} = a, a \geq 0

2^{2} = 2

= 2

= \frac{1}{2}

- \frac{1}{4} = - \frac{1}{2}

- \frac{1}{4}

Aplicar las leyes de los exponentes:

\frac{a}{b} = \frac{a}{b}, a \geq 0, b \geq 0

= - \frac{1}{4}

Aplicar las leyes de los exponentes:

1 = 1

1 = 1

= - \frac{1}{4}

4 = 2

4

Descomponer el número en factores primos:

4 = 2^{2}

= 2^{2}

Aplicar las leyes de los exponentes:

a^{2} = a, a \geq 0

2^{2} = 2

= 2

= - \frac{1}{2}

x = \frac{1}{2}, x = - \frac{1}{2}

x = \frac{1}{2}, x = - \frac{1}{2}

Verificar las soluciones:

x = \frac{1}{2}

Verdadero

, x = - \frac{1}{2}

Verdadero

Verificar las soluciones sustituyéndolas en

2 xx - (1 - (2 x)^{2}) (1 - x^{2}) = \frac{1}{2}

Quitar las que no concuerden con la ecuación.

Sustituir

x = \frac{1}{2} :

Verdadero

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

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

2 (\frac{1}{2}) (\frac{1}{2}) - (1 - (2 (\frac{1}{2}))^{2}) (1 - (\frac{1}{2})^{2})

Quitar los parentesis:

(a) = a

= 2 \cdot \frac{1}{2} \cdot \frac{1}{2} - (1 - (2 \cdot \frac{1}{2})^{2}) (1 - (\frac{1}{2})^{2})

2 \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{2}

2 \cdot \frac{1}{2} \cdot \frac{1}{2}

Multiplicar fracciones:

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

= \frac{1 \cdot 1 \cdot 2}{2 \cdot 2}

Eliminar los terminos comunes:

2

= \frac{1 \cdot 1}{2}

Multiplicar los numeros:

1 \cdot 1 = 1

= \frac{1}{2}

(1 - (2 \cdot \frac{1}{2})^{2}) (1 - (\frac{1}{2})^{2}) = 0

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

(2 \cdot \frac{1}{2})^{2} = 1

(2 \cdot \frac{1}{2})^{2}

Multiplicar

2 \cdot \frac{1}{2} : 1

2 \cdot \frac{1}{2}

Multiplicar fracciones:

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

= \frac{1 \cdot 2}{2}

Eliminar los terminos comunes:

2

= 1

= 1^{2}

Aplicar la regla

1^{a} = 1

= 1

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

(\frac{1}{2})^{2} = \frac{1}{4}

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

Aplicar las leyes de los exponentes:

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

= \frac{1 ^{2}}{2 ^{2}}

Aplicar la regla

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

2^{2} = 4

= \frac{1}{4}

= (1 - 1) (- \frac{1}{4} + 1)

Restar:

1 - 1 = 0

= 0 \cdot (- \frac{1}{4} + 1)

Simplificar

1 - \frac{1}{4}

en una fracción:

\frac{3}{4}

1 - \frac{1}{4}

Convertir a fracción:

1 = \frac{1 \cdot 4}{4}

= \frac{1 \cdot 4}{4} - \frac{1}{4}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{1 \cdot 4 - 1}{4}

1 \cdot 4 - 1 = 3

1 \cdot 4 - 1

Multiplicar los numeros:

1 \cdot 4 = 4

= 4 - 1

Restar:

4 - 1 = 3

= 3

= \frac{3}{4}

= 0 \cdot \frac{3}{4}

Aplicar la regla

0 \cdot a = 0

= 0

Aplicar la regla

0 = 0

= 0

= \frac{1}{2} - 0

\frac{1}{2} - 0 = \frac{1}{2}

= \frac{1}{2}

\frac{1}{2} = \frac{1}{2}

Verdadero

Sustituir

x = - \frac{1}{2} :

Verdadero

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

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

2 (- \frac{1}{2}) (- \frac{1}{2}) - (1 - (2 (- \frac{1}{2}))^{2}) (1 - (- \frac{1}{2})^{2})

Quitar los parentesis:

(- a) = - a, - (- a) = a

= 2 \cdot \frac{1}{2} \cdot \frac{1}{2} - (1 - (- 2 \cdot \frac{1}{2})^{2}) (1 - (- \frac{1}{2})^{2})

2 \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{2}

2 \cdot \frac{1}{2} \cdot \frac{1}{2}

Multiplicar fracciones:

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

= \frac{1 \cdot 1 \cdot 2}{2 \cdot 2}

Eliminar los terminos comunes:

2

= \frac{1 \cdot 1}{2}

Multiplicar los numeros:

1 \cdot 1 = 1

= \frac{1}{2}

(1 - (- 2 \cdot \frac{1}{2})^{2}) (1 - (- \frac{1}{2})^{2}) = 0

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

(- 2 \cdot \frac{1}{2})^{2} = 1

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

Multiplicar

- 2 \cdot \frac{1}{2} : - 1

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

Multiplicar fracciones:

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

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

Eliminar los terminos comunes:

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

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

(- \frac{1}{2})^{2} = \frac{1}{4}

(- \frac{1}{2})^{2}

Aplicar las leyes de los exponentes:

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

n

es par

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

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

Aplicar las leyes de los exponentes:

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

= \frac{1 ^{2}}{2 ^{2}}

Aplicar la regla

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

2^{2} = 4

= \frac{1}{4}

= (1 - 1) (- \frac{1}{4} + 1)

Restar:

1 - 1 = 0

= 0 \cdot (- \frac{1}{4} + 1)

Simplificar

1 - \frac{1}{4}

en una fracción:

\frac{3}{4}

1 - \frac{1}{4}

Convertir a fracción:

1 = \frac{1 \cdot 4}{4}

= \frac{1 \cdot 4}{4} - \frac{1}{4}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{1 \cdot 4 - 1}{4}

1 \cdot 4 - 1 = 3

1 \cdot 4 - 1

Multiplicar los numeros:

1 \cdot 4 = 4

= 4 - 1

Restar:

4 - 1 = 3

= 3

= \frac{3}{4}

= 0 \cdot \frac{3}{4}

Aplicar la regla

0 \cdot a = 0

= 0

Aplicar la regla

0 = 0

= 0

= \frac{1}{2} - 0

\frac{1}{2} - 0 = \frac{1}{2}

= \frac{1}{2}

\frac{1}{2} = \frac{1}{2}

Verdadero

Las soluciones son

x = \frac{1}{2}, x = - \frac{1}{2}

x = \frac{1}{2}, x = - \frac{1}{2}

Verificar las soluciones sustituyendo en la ecuación original

Verificar las soluciones sustituyéndolas en

arccos (2 x) + arccos (x) = \frac{π}{3}

Quitar las que no concuerden con la ecuación.

Verificar la solución

\frac{1}{2} :

Verdadero

\frac{1}{2}

Sustituir

n = 1

\frac{1}{2}

Multiplicar

arccos (2 x) + arccos (x) = \frac{π}{3}

por

x = \frac{1}{2}

arccos (2 \cdot \frac{1}{2}) + arccos (\frac{1}{2}) = \frac{π}{3}

Simplificar

1.04719 \dots = 1.04719 \dots

\Rightarrow Verdadero

Verificar la solución

- \frac{1}{2} :

Falso

- \frac{1}{2}

Sustituir

n = 1

- \frac{1}{2}

Multiplicar

arccos (2 x) + arccos (x) = \frac{π}{3}

por

x = - \frac{1}{2}

arccos (2 (- \frac{1}{2})) + arccos (- \frac{1}{2}) = \frac{π}{3}

Simplificar

5.23598 \dots = 1.04719 \dots

\Rightarrow Falso

x = \frac{1}{2}

Gráfica

Ejemplos populares

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