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Popular >

-arccos(x)+arctan(5/12)=0

Solución

- arccos (x) + arctan (\frac{5}{12}) = 0

Solución

x = \frac{12}{13}

Pasos de solución

- arccos (x) + arctan (\frac{5}{12}) = 0

Mover

arctan (\frac{5}{12})

al lado derecho

- arccos (x) + arctan (\frac{5}{12}) = 0

Restar

arctan (\frac{5}{12})

de ambos lados

- arccos (x) + arctan (\frac{5}{12}) - arctan (\frac{5}{12}) = 0 - arctan (\frac{5}{12})

Simplificar

- arccos (x) = - arctan (\frac{5}{12})

- arccos (x) = - arctan (\frac{5}{12})

Dividir ambos lados entre

- 1

- arccos (x) = - arctan (\frac{5}{12})

Dividir ambos lados entre

- 1

\frac{- arccos ( x )}{- 1} = \frac{- arctan ( \frac{5}{12} )}{- 1}

Simplificar

\frac{- arccos ( x )}{- 1} = \frac{- arctan ( \frac{5}{12} )}{- 1}

Simplificar

\frac{- arccos ( x )}{- 1} : arccos (x)

\frac{- arccos ( x )}{- 1}

Aplicar las propiedades de las fracciones:

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

= \frac{arccos ( x )}{1}

Aplicar la regla

\frac{a}{1} = a

= arccos (x)

Simplificar

\frac{- arctan ( \frac{5}{12} )}{- 1} : arctan (\frac{5}{12})

\frac{- arctan ( \frac{5}{12} )}{- 1}

Aplicar las propiedades de las fracciones:

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

= \frac{arctan ( \frac{5}{12} )}{1}

Aplicar las propiedades de las fracciones:

\frac{a}{1} = a

= arctan (\frac{5}{12})

arccos (x) = arctan (\frac{5}{12})

arccos (x) = arctan (\frac{5}{12})

arccos (x) = arctan (\frac{5}{12})

Aplicar propiedades trigonométricas inversas

arccos (x) = arctan (\frac{5}{12})

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

x = cos (arctan (\frac{5}{12}))

cos (arctan (\frac{5}{12})) = \frac{12}{13}

cos (arctan (\frac{5}{12}))

Re-escribir usando identidades trigonométricas:

cos (arctan (\frac{5}{12})) = \frac{1 + ( \frac{5}{12} ) ^{2}}{1 + ( \frac{5}{12} ) ^{2}}

Usar la siguiente identidad:

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

= \frac{1 + ( \frac{5}{12} ) ^{2}}{1 + ( \frac{5}{12} ) ^{2}}

= \frac{1 + ( \frac{5}{12} ) ^{2}}{1 + ( \frac{5}{12} ) ^{2}}

Simplificar

= \frac{12}{13}

x = \frac{12}{13}

x = \frac{12}{13}

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