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cos(76)sec(8x+4)=1

Solución

cos (7 6^{\circ}) sec (8 x + 4) = 1

Solución

x = - \frac{1}{2} + \frac{18 0 ^{\circ} n}{4} + \frac{1.32645 \dots}{8}, x = - \frac{1}{2} + 4 5^{\circ} + \frac{18 0 ^{\circ} n}{4} - \frac{1.32645 \dots}{8}

radianes

x = - \frac{1}{2} + \frac{1.32645 \dots}{8} + \frac{π}{4} n, x = - \frac{1}{2} + \frac{π}{4} - \frac{1.32645 \dots}{8} + \frac{π}{4} n

Pasos de solución

cos (7 6^{\circ}) sec (8 x + 4) = 1

Dividir ambos lados entre

cos (7 6^{\circ})

cos (7 6^{\circ}) sec (8 x + 4) = 1

Dividir ambos lados entre

cos (7 6^{\circ})

\frac{cos ( 7 6 ^{\circ} ) sec ( 8 x + 4 )}{cos ( 7 6 ^{\circ} )} = \frac{1}{cos ( 7 6 ^{\circ} )}

Simplificar

sec (8 x + 4) = \frac{1}{cos ( 7 6 ^{\circ} )}

sec (8 x + 4) = \frac{1}{cos ( 7 6 ^{\circ} )}

Aplicar propiedades trigonométricas inversas

sec (8 x + 4) = \frac{1}{cos ( 7 6 ^{\circ} )}

Soluciones generales para

sec (8 x + 4) = \frac{1}{cos ( 7 6 ^{\circ} )}

sec (x) = a \Rightarrow x = arcsec (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arcsec (a) + 36 0^{\circ} n

8 x + 4 = arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n, 8 x + 4 = 36 0^{\circ} - arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n

8 x + 4 = arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n, 8 x + 4 = 36 0^{\circ} - arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n

Resolver

8 x + 4 = arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n : x = - \frac{1}{2} + \frac{18 0 ^{\circ} n}{4} + \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

8 x + 4 = arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n

Mover

4

al lado derecho

8 x + 4 = arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n

Restar

4

de ambos lados

8 x + 4 - 4 = arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n - 4

Simplificar

8 x = arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n - 4

8 x = arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n - 4

Dividir ambos lados entre

8

8 x = arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n - 4

Dividir ambos lados entre

8

\frac{8 x}{8} = \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8} + \frac{36 0 ^{\circ} n}{8} - \frac{4}{8}

Simplificar

\frac{8 x}{8} = \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8} + \frac{36 0 ^{\circ} n}{8} - \frac{4}{8}

Simplificar

\frac{8 x}{8} : x

\frac{8 x}{8}

Dividir:

\frac{8}{8} = 1

= x

Simplificar

\frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8} + \frac{36 0 ^{\circ} n}{8} - \frac{4}{8} : - \frac{1}{2} + \frac{18 0 ^{\circ} n}{4} + \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

\frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8} + \frac{36 0 ^{\circ} n}{8} - \frac{4}{8}

Agrupar términos semejantes

= - \frac{4}{8} + \frac{36 0 ^{\circ} n}{8} + \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

Cancelar

\frac{4}{8} : \frac{1}{2}

\frac{4}{8}

Eliminar los terminos comunes:

4

= \frac{1}{2}

= - \frac{1}{2} + \frac{36 0 ^{\circ} n}{8} + \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

Cancelar

\frac{36 0 ^{\circ} n}{8} : \frac{18 0 ^{\circ} n}{4}

\frac{36 0 ^{\circ} n}{8}

Eliminar los terminos comunes:

2

= \frac{18 0 ^{\circ} n}{4}

= - \frac{1}{2} + \frac{18 0 ^{\circ} n}{4} + \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

x = - \frac{1}{2} + \frac{18 0 ^{\circ} n}{4} + \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

x = - \frac{1}{2} + \frac{18 0 ^{\circ} n}{4} + \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

x = - \frac{1}{2} + \frac{18 0 ^{\circ} n}{4} + \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

Resolver

8 x + 4 = 36 0^{\circ} - arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n : x = - \frac{1}{2} + 4 5^{\circ} + \frac{18 0 ^{\circ} n}{4} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

8 x + 4 = 36 0^{\circ} - arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n

Mover

4

al lado derecho

8 x + 4 = 36 0^{\circ} - arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n

Restar

4

de ambos lados

8 x + 4 - 4 = 36 0^{\circ} - arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n - 4

Simplificar

8 x = 36 0^{\circ} - arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n - 4

8 x = 36 0^{\circ} - arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n - 4

Dividir ambos lados entre

8

8 x = 36 0^{\circ} - arcsec (\frac{1}{cos ( 7 6 ^{\circ} )}) + 36 0^{\circ} n - 4

Dividir ambos lados entre

8

\frac{8 x}{8} = 4 5^{\circ} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8} + \frac{36 0 ^{\circ} n}{8} - \frac{4}{8}

Simplificar

\frac{8 x}{8} = 4 5^{\circ} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8} + \frac{36 0 ^{\circ} n}{8} - \frac{4}{8}

Simplificar

\frac{8 x}{8} : x

\frac{8 x}{8}

Dividir:

\frac{8}{8} = 1

= x

Simplificar

4 5^{\circ} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8} + \frac{36 0 ^{\circ} n}{8} - \frac{4}{8} : - \frac{1}{2} + 4 5^{\circ} + \frac{18 0 ^{\circ} n}{4} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

4 5^{\circ} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8} + \frac{36 0 ^{\circ} n}{8} - \frac{4}{8}

Agrupar términos semejantes

= - \frac{4}{8} + 4 5^{\circ} + \frac{36 0 ^{\circ} n}{8} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

Cancelar

\frac{4}{8} : \frac{1}{2}

\frac{4}{8}

Eliminar los terminos comunes:

4

= \frac{1}{2}

= - \frac{1}{2} + 4 5^{\circ} + \frac{36 0 ^{\circ} n}{8} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

Cancelar

4 5^{\circ} : 4 5^{\circ}

4 5^{\circ}

Eliminar los terminos comunes:

2

= 4 5^{\circ}

= - \frac{1}{2} + 4 5^{\circ} + \frac{36 0 ^{\circ} n}{8} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

Cancelar

\frac{36 0 ^{\circ} n}{8} : \frac{18 0 ^{\circ} n}{4}

\frac{36 0 ^{\circ} n}{8}

Eliminar los terminos comunes:

2

= \frac{18 0 ^{\circ} n}{4}

= - \frac{1}{2} + 4 5^{\circ} + \frac{18 0 ^{\circ} n}{4} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

x = - \frac{1}{2} + 4 5^{\circ} + \frac{18 0 ^{\circ} n}{4} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

x = - \frac{1}{2} + 4 5^{\circ} + \frac{18 0 ^{\circ} n}{4} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

x = - \frac{1}{2} + 4 5^{\circ} + \frac{18 0 ^{\circ} n}{4} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

x = - \frac{1}{2} + \frac{18 0 ^{\circ} n}{4} + \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}, x = - \frac{1}{2} + 4 5^{\circ} + \frac{18 0 ^{\circ} n}{4} - \frac{arcsec ( \frac{1}{c o s ( 7 6 ^{\circ} )} )}{8}

Mostrar soluciones en forma decimal

x = - \frac{1}{2} + \frac{18 0 ^{\circ} n}{4} + \frac{1.32645 \dots}{8}, x = - \frac{1}{2} + 4 5^{\circ} + \frac{18 0 ^{\circ} n}{4} - \frac{1.32645 \dots}{8}

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