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sin^2(x)=((5m-7))/6

Solución

sin^{2} (x) = \frac{( 5 m - 7 )}{6}

x = arcsin (\frac{5 m - 7}{6}) + 2 πn, x = π + arcsin (- \frac{5 m - 7}{6}) + 2 πn, x = arcsin (- \frac{5 m - 7}{6}) + 2 πn, x = π + arcsin (\frac{5 m - 7}{6}) + 2 πn

Pasos de solución

sin^{2} (x) = \frac{( 5 m - 7 )}{6}

Usando el método de sustitución

sin^{2} (x) = \frac{5 m - 7}{6}

Sea:

sin (x) = u

u^{2} = \frac{5 m - 7}{6}

u^{2} = \frac{5 m - 7}{6} : u = \frac{5 m - 7}{6}, u = - \frac{5 m - 7}{6}

u^{2} = \frac{5 m - 7}{6}

Para

x^{2} = f (a)

las soluciones son

x = f (a), - f (a)

u = \frac{5 m - 7}{6}, u = - \frac{5 m - 7}{6}

Sustituir en la ecuación

u = sin (x)

sin (x) = \frac{5 m - 7}{6}, sin (x) = - \frac{5 m - 7}{6}

sin (x) = \frac{5 m - 7}{6}, sin (x) = - \frac{5 m - 7}{6}

sin (x) = \frac{5 m - 7}{6} : x = arcsin (\frac{5 m - 7}{6}) + 2 πn, x = π + arcsin (- \frac{5 m - 7}{6}) + 2 πn

sin (x) = \frac{5 m - 7}{6}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{5 m - 7}{6}

Soluciones generales para

sin (x) = \frac{5 m - 7}{6}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (\frac{5 m - 7}{6}) + 2 πn, x = π + arcsin (- \frac{5 m - 7}{6}) + 2 πn

x = arcsin (\frac{5 m - 7}{6}) + 2 πn, x = π + arcsin (- \frac{5 m - 7}{6}) + 2 πn

sin (x) = - \frac{5 m - 7}{6} : x = arcsin (- \frac{5 m - 7}{6}) + 2 πn, x = π + arcsin (\frac{5 m - 7}{6}) + 2 πn

sin (x) = - \frac{5 m - 7}{6}

Aplicar propiedades trigonométricas inversas

sin (x) = - \frac{5 m - 7}{6}

Soluciones generales para

sin (x) = - \frac{5 m - 7}{6}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{5 m - 7}{6}) + 2 πn, x = π + arcsin (\frac{5 m - 7}{6}) + 2 πn

x = arcsin (- \frac{5 m - 7}{6}) + 2 πn, x = π + arcsin (\frac{5 m - 7}{6}) + 2 πn

Combinar toda las soluciones

x = arcsin (\frac{5 m - 7}{6}) + 2 πn, x = π + arcsin (- \frac{5 m - 7}{6}) + 2 πn, x = arcsin (- \frac{5 m - 7}{6}) + 2 πn, x = π + arcsin (\frac{5 m - 7}{6}) + 2 πn