English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2= 1/(cos^2(x))

Solución

2 = \frac{1}{cos ^{2} ( x )}

Solución

x = 0.78539 \dots + 2 πn, x = 2 π - 0.78539 \dots + 2 πn, x = 2.35619 \dots + 2 πn, x = - 2.35619 \dots + 2 πn

Grados

x = 4 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n, x = - 13 5^{\circ} + 36 0^{\circ} n

Pasos de solución

2 = \frac{1}{cos ^{2} ( x )}

Intercambiar lados

\frac{1}{cos ^{2} ( x )} = 2

Usando el método de sustitución

\frac{1}{cos ^{2} ( x )} = 2

Sea:

cos (x) = u

\frac{1}{u ^{2}} = 2

\frac{1}{u ^{2}} = 2 : u = \frac{1}{2}, u = - \frac{1}{2}

\frac{1}{u ^{2}} = 2

Multiplicar ambos lados por

u^{2}

\frac{1}{u ^{2}} = 2

Multiplicar ambos lados por

u^{2}

\frac{1}{u ^{2}} u^{2} = 2 u^{2}

Simplificar

1 = 2 u^{2}

1 = 2 u^{2}

Resolver

1 = 2 u^{2} : u = \frac{1}{2}, u = - \frac{1}{2}

1 = 2 u^{2}

Intercambiar lados

2 u^{2} = 1

Dividir ambos lados entre

2

2 u^{2} = 1

Dividir ambos lados entre

2

\frac{2 u ^{2}}{2} = \frac{1}{2}

Simplificar

u^{2} = \frac{1}{2}

u^{2} = \frac{1}{2}

Para

x^{2} = f (a)

las soluciones son

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

u = \frac{1}{2}, u = - \frac{1}{2}

u = \frac{1}{2}, u = - \frac{1}{2}

Verificar las soluciones

Encontrar los puntos no definidos (singularidades):

u = 0

Tomar el(los) denominador(es) de

\frac{1}{u ^{2}}

y comparar con cero

Resolver

u^{2} = 0 : u = 0

u^{2} = 0

Aplicar la regla

x^{n} = 0 \Rightarrow x = 0

u = 0

Los siguientes puntos no están definidos

u = 0

Combinar los puntos no definidos con las soluciones:

u = \frac{1}{2}, u = - \frac{1}{2}

Sustituir en la ecuación

u = cos (x)

cos (x) = \frac{1}{2}, cos (x) = - \frac{1}{2}

cos (x) = \frac{1}{2}, cos (x) = - \frac{1}{2}

cos (x) = \frac{1}{2} : x = arccos (\frac{1}{2}) + 2 πn, x = 2 π - arccos (\frac{1}{2}) + 2 πn

cos (x) = \frac{1}{2}

Aplicar propiedades trigonométricas inversas

cos (x) = \frac{1}{2}

Soluciones generales para

cos (x) = \frac{1}{2}

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

x = arccos (\frac{1}{2}) + 2 πn, x = 2 π - arccos (\frac{1}{2}) + 2 πn

x = arccos (\frac{1}{2}) + 2 πn, x = 2 π - arccos (\frac{1}{2}) + 2 πn

cos (x) = - \frac{1}{2} : x = arccos (- \frac{1}{2}) + 2 πn, x = - arccos (- \frac{1}{2}) + 2 πn

cos (x) = - \frac{1}{2}

Aplicar propiedades trigonométricas inversas

cos (x) = - \frac{1}{2}

Soluciones generales para

cos (x) = - \frac{1}{2}

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

x = arccos (- \frac{1}{2}) + 2 πn, x = - arccos (- \frac{1}{2}) + 2 πn

x = arccos (- \frac{1}{2}) + 2 πn, x = - arccos (- \frac{1}{2}) + 2 πn

Combinar toda las soluciones

x = arccos (\frac{1}{2}) + 2 πn, x = 2 π - arccos (\frac{1}{2}) + 2 πn, x = arccos (- \frac{1}{2}) + 2 πn, x = - arccos (- \frac{1}{2}) + 2 πn

Mostrar soluciones en forma decimal

x = 0.78539 \dots + 2 πn, x = 2 π - 0.78539 \dots + 2 πn, x = 2.35619 \dots + 2 πn, x = - 2.35619 \dots + 2 πn

Ejemplos populares

arccot(x-2)=arccot(x-1)+arccot(x)

arccot (x - 2) = arccot (x - 1) + arccot (x)

tan(x)-2/(tan(x))=1

tan (x) - \frac{2}{tan ( x )} = 1

sin(x)+sqrt(3)cos(x)=sqrt(2)

sin (x) + 3 cos (x) = 2

arccos(2x)=pi

arccos (2 x) = π

(cosh(0.2m))/(cosh(0.4m))=0.6

\frac{cosh ( 0.2 m )}{cosh ( 0.4 m )} = 0.6