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solvefor x,c^2=a^2+b^2-2ab*cos(x)

Solución

resolver para

x, c^{2} = a^{2} + b^{2} - 2 ab \cdot cos (x)

Solución

x = arccos (- \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}) + 2 πn, x = - arccos (- \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}) + 2 πn

Pasos de solución

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

Intercambiar lados

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

Mover

a^{2}

al lado derecho

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

Restar

a^{2}

de ambos lados

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

Simplificar

b^{2} - 2 ab cos (x) = c^{2} - a^{2}

b^{2} - 2 ab cos (x) = c^{2} - a^{2}

Mover

b^{2}

al lado derecho

b^{2} - 2 ab cos (x) = c^{2} - a^{2}

Restar

b^{2}

de ambos lados

b^{2} - 2 ab cos (x) - b^{2} = c^{2} - a^{2} - b^{2}

Simplificar

- 2 ab cos (x) = c^{2} - a^{2} - b^{2}

- 2 ab cos (x) = c^{2} - a^{2} - b^{2}

Dividir ambos lados entre

- 2 ab; - 2 ab \neq = 0

- 2 ab cos (x) = c^{2} - a^{2} - b^{2}

Dividir ambos lados entre

- 2 ab; - 2 ab \neq = 0

\frac{- 2 ab cos ( x )}{- 2 ab} = \frac{c ^{2}}{- 2 ab} - \frac{a ^{2}}{- 2 ab} - \frac{b ^{2}}{- 2 ab}; - 2 ab \neq = 0

Simplificar

\frac{- 2 ab cos ( x )}{- 2 ab} = \frac{c ^{2}}{- 2 ab} - \frac{a ^{2}}{- 2 ab} - \frac{b ^{2}}{- 2 ab}

Simplificar

\frac{- 2 ab cos ( x )}{- 2 ab} : cos (x)

\frac{- 2 ab cos ( x )}{- 2 ab}

Aplicar las propiedades de las fracciones:

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

= \frac{2 ab cos ( x )}{2 ab}

Dividir:

\frac{2}{2} = 1

= \frac{ab cos ( x )}{ab}

Eliminar los terminos comunes:

a

= \frac{b cos ( x )}{b}

Eliminar los terminos comunes:

b

= cos (x)

Simplificar

\frac{c ^{2}}{- 2 ab} - \frac{a ^{2}}{- 2 ab} - \frac{b ^{2}}{- 2 ab} : - \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}

\frac{c ^{2}}{- 2 ab} - \frac{a ^{2}}{- 2 ab} - \frac{b ^{2}}{- 2 ab}

Aplicar la regla

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

= \frac{c ^{2} - a ^{2} - b ^{2}}{- 2 ab}

Aplicar las propiedades de las fracciones:

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

= - \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}

cos (x) = - \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}; - 2 ab \neq = 0

cos (x) = - \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}; - 2 ab \neq = 0

cos (x) = - \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}; - 2 ab \neq = 0

Aplicar propiedades trigonométricas inversas

cos (x) = - \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}

Soluciones generales para

cos (x) = - \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

x = arccos (- \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}) + 2 πn, x = - arccos (- \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}) + 2 πn

x = arccos (- \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}) + 2 πn, x = - arccos (- \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}) + 2 πn

Ejemplos populares

sin(-pi/8 c)=-14/14

sin (- \frac{π}{8} c) = - \frac{14}{14}

(25)/(sin(x))=(18)/(sin(36))

\frac{25}{sin ( x )} = \frac{18}{sin ( 3 6 ^{\circ} )}

7tan(3x)-21tan(x)=0

7 tan (3 x) - 21 tan (x) = 0

cos (A) = - \frac{3}{25}

tan (a) = \frac{12}{5}