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a^2=b^2+c^2-2bc*cos(x)

Solución

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

Solución

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

Pasos de solución

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

Intercambiar lados

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

Mover

b^{2}

al lado derecho

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

Restar

b^{2}

de ambos lados

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

Simplificar

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

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

Mover

c^{2}

al lado derecho

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

Restar

c^{2}

de ambos lados

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

Simplificar

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

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

Dividir ambos lados entre

- 2 b c; - 2 b c \neq = 0

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

Dividir ambos lados entre

- 2 b c; - 2 b c \neq = 0

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

Simplificar

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

Simplificar

\frac{- 2 b c cos ( x )}{- 2 b c} : cos (x)

\frac{- 2 b c cos ( x )}{- 2 b c}

Aplicar las propiedades de las fracciones:

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

= \frac{2 b c cos ( x )}{2 b c}

Dividir:

\frac{2}{2} = 1

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

Eliminar los terminos comunes:

b

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

Eliminar los terminos comunes:

c

= cos (x)

Simplificar

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

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

Aplicar la regla

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

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

Aplicar las propiedades de las fracciones:

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

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

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

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

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

Aplicar propiedades trigonométricas inversas

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

Soluciones generales para

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

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

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

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

Ejemplos populares

3sin^2(X)-cos(X)=0

3 sin^{2} (X) - cos (X) = 0

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6sin^2(a)+cos(2a)=2

6 sin^{2} (a) + cos (2 a) = 2

cos^{(2)}(x)+sin(x)=1

cos^{(2)} (x) + sin (x) = 1