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2arctan(1/2)-arctan(x)= pi/4

Solución

2 arctan (\frac{1}{2}) - arctan (x) = \frac{π}{4}

x = tan (\frac{8 \cdot 0.46364 \dots - π}{4})

Pasos de solución

2 arctan (\frac{1}{2}) - arctan (x) = \frac{π}{4}

Mover

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

al lado derecho

2 arctan (\frac{1}{2}) - arctan (x) = \frac{π}{4}

Restar

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

de ambos lados

2 arctan (\frac{1}{2}) - arctan (x) - 2 arctan (\frac{1}{2}) = \frac{π}{4} - 2 arctan (\frac{1}{2})

Simplificar

- arctan (x) = \frac{π}{4} - 2 arctan (\frac{1}{2})

- arctan (x) = \frac{π}{4} - 2 arctan (\frac{1}{2})

Dividir ambos lados entre

- 1

- arctan (x) = \frac{π}{4} - 2 arctan (\frac{1}{2})

Dividir ambos lados entre

- 1

\frac{- arctan ( x )}{- 1} = \frac{\frac{π}{4}}{- 1} - \frac{2 arctan ( \frac{1}{2} )}{- 1}

Simplificar

\frac{- arctan ( x )}{- 1} = \frac{\frac{π}{4}}{- 1} - \frac{2 arctan ( \frac{1}{2} )}{- 1}

Simplificar

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

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

Aplicar las propiedades de las fracciones:

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

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

Aplicar la regla

\frac{a}{1} = a

= arctan (x)

Simplificar

\frac{\frac{π}{4}}{- 1} - \frac{2 arctan ( \frac{1}{2} )}{- 1} : \frac{8 arctan ( \frac{1}{2} ) - π}{4}

\frac{\frac{π}{4}}{- 1} - \frac{2 arctan ( \frac{1}{2} )}{- 1}

Aplicar la regla

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

= \frac{\frac{π}{4} - 2 arctan ( \frac{1}{2} )}{- 1}

Aplicar las propiedades de las fracciones:

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

\frac{π}{4} - 2 arctan (\frac{1}{2}) = - (2 arctan (\frac{1}{2}) - \frac{π}{4})

= \frac{2 arctan ( \frac{1}{2} ) - \frac{π}{4}}{1}

Simplificar

2 arctan (\frac{1}{2}) - \frac{π}{4}

en una fracción:

\frac{8 arctan ( \frac{1}{2} ) - π}{4}

2 arctan (\frac{1}{2}) - \frac{π}{4}

Convertir a fracción:

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

= \frac{2 arctan ( \frac{1}{2} ) \cdot 4}{4} - \frac{π}{4}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{2 arctan ( \frac{1}{2} ) \cdot 4 - π}{4}

Multiplicar los numeros:

2 \cdot 4 = 8

= \frac{8 arctan ( \frac{1}{2} ) - π}{4}

= \frac{\frac{8 a r c t a n ( \frac{1}{2} ) - π}{4}}{1}

Aplicar las propiedades de las fracciones:

\frac{a}{1} = a

= \frac{8 arctan ( \frac{1}{2} ) - π}{4}

arctan (x) = \frac{8 arctan ( \frac{1}{2} ) - π}{4}

arctan (x) = \frac{8 arctan ( \frac{1}{2} ) - π}{4}

arctan (x) = \frac{8 arctan ( \frac{1}{2} ) - π}{4}

Aplicar propiedades trigonométricas inversas

arctan (x) = \frac{8 arctan ( \frac{1}{2} ) - π}{4}

arctan (x) = a \Rightarrow x = tan (a)

x = tan (\frac{8 arctan ( \frac{1}{2} ) - π}{4})

x = tan (\frac{8 arctan ( \frac{1}{2} ) - π}{4})

Mostrar soluciones en forma decimal

x = tan (\frac{8 \cdot 0.46364 \dots - π}{4})

cos (x) = (2 - tan (x)) (1 + sin (x))

sin (θ) = \frac{13}{85}

sin (2 x) = \frac{( 6 m - 5 )}{8}

cos (θ) = \frac{3}{45}

cos^{2} (x) = \frac{9}{16}