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solvefor c,e=r(sec(c/2)-1)

Solución

resolver para

c, e = r (sec (\frac{c}{2}) - 1)

Solución

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn, c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

Pasos de solución

e = r (sec (\frac{c}{2}) - 1)

Intercambiar lados

r (sec (\frac{c}{2}) - 1) = e

Dividir ambos lados entre

r; r \neq = 0

r (sec (\frac{c}{2}) - 1) = e

Dividir ambos lados entre

r; r \neq = 0

\frac{r ( sec ( \frac{c}{2} ) - 1 )}{r} = \frac{e}{r}; r \neq = 0

Simplificar

sec (\frac{c}{2}) - 1 = \frac{e}{r}; r \neq = 0

sec (\frac{c}{2}) - 1 = \frac{e}{r}; r \neq = 0

Mover

1

al lado derecho

sec (\frac{c}{2}) - 1 = \frac{e}{r}; r \neq = 0

Sumar

1

a ambos lados

sec (\frac{c}{2}) - 1 + 1 = \frac{e}{r} + 1; r \neq = 0

Simplificar

sec (\frac{c}{2}) = \frac{e}{r} + 1; r \neq = 0

sec (\frac{c}{2}) = \frac{e}{r} + 1; r \neq = 0

Aplicar propiedades trigonométricas inversas

sec (\frac{c}{2}) = \frac{e}{r} + 1

Soluciones generales para

sec (\frac{c}{2}) = \frac{e}{r} + 1

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = - arcsec (a) + 2 πn

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn, \frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn, \frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

Resolver

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn : c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn

Multiplicar ambos lados por

2

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn

Multiplicar ambos lados por

2

\frac{2 c}{2} = 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

Simplificar

\frac{2 c}{2} = 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

Simplificar

\frac{2 c}{2} : c

\frac{2 c}{2}

Dividir:

\frac{2}{2} = 1

= c

Simplificar

2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn : 2 arcsec (\frac{e}{r} + 1) + 4 πn

2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

Multiplicar los numeros:

2 \cdot 2 = 4

= 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

Resolver

\frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn : c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

\frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

Multiplicar ambos lados por

2

\frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

Multiplicar ambos lados por

2

\frac{2 c}{2} = - 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

Simplificar

\frac{2 c}{2} = - 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

Simplificar

\frac{2 c}{2} : c

\frac{2 c}{2}

Dividir:

\frac{2}{2} = 1

= c

Simplificar

- 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn : - 2 arcsec (\frac{e}{r} + 1) + 4 πn

- 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

Multiplicar los numeros:

2 \cdot 2 = 4

= - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn, c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

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