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Popular >

cos(2x)csc^2(x)=2cos(2x)

Solución

cos (2 x) csc^{2} (x) = 2 cos (2 x)

Solución

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Grados

x = 4 5^{\circ} + 18 0^{\circ} n, x = 13 5^{\circ} + 18 0^{\circ} n

Pasos de solución

cos (2 x) csc^{2} (x) = 2 cos (2 x)

Restar

2 cos (2 x)

de ambos lados

csc^{2} (x) cos (2 x) - 2 cos (2 x) = 0

Factorizar

csc^{2} (x) cos (2 x) - 2 cos (2 x) : cos (2 x) (csc (x) + 2) (csc (x) - 2)

csc^{2} (x) cos (2 x) - 2 cos (2 x)

Factorizar el termino común

cos (2 x)

= cos (2 x) (csc^{2} (x) - 2)

Factorizar

csc^{2} (x) - 2 : (csc (x) + 2) (csc (x) - 2)

csc^{2} (x) - 2

Aplicar las leyes de los exponentes:

a = (a)^{2}

2 = (2)^{2}

= csc^{2} (x) - (2)^{2}

Aplicar la siguiente regla para binomios al cuadrado:

x^{2} - y^{2} = (x + y) (x - y)

csc^{2} (x) - (2)^{2} = (csc (x) + 2) (csc (x) - 2)

= (csc (x) + 2) (csc (x) - 2)

= cos (2 x) (csc (x) + 2) (csc (x) - 2)

cos (2 x) (csc (x) + 2) (csc (x) - 2) = 0

Resolver cada parte por separado

cos (2 x) = 0 or csc (x) + 2 = 0 or csc (x) - 2 = 0

cos (2 x) = 0 : x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

cos (2 x) = 0

Soluciones generales para

cos (2 x) = 0

cos (x)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

2 x = \frac{π}{2} + 2 πn, 2 x = \frac{3 π}{2} + 2 πn

2 x = \frac{π}{2} + 2 πn, 2 x = \frac{3 π}{2} + 2 πn

Resolver

2 x = \frac{π}{2} + 2 πn : x = \frac{π}{4} + πn

2 x = \frac{π}{2} + 2 πn

Dividir ambos lados entre

2

2 x = \frac{π}{2} + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{\frac{π}{2}}{2} + \frac{2 πn}{2}

Simplificar

\frac{2 x}{2} = \frac{\frac{π}{2}}{2} + \frac{2 πn}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{\frac{π}{2}}{2} + \frac{2 πn}{2} : \frac{π}{4} + πn

\frac{\frac{π}{2}}{2} + \frac{2 πn}{2}

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{π}{4}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

= \frac{π}{4} + πn

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

Resolver

2 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{4} + πn

2 x = \frac{3 π}{2} + 2 πn

Dividir ambos lados entre

2

2 x = \frac{3 π}{2} + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2}

Simplificar

\frac{2 x}{2} = \frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2} : \frac{3 π}{4} + πn

\frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2}

\frac{\frac{3 π}{2}}{2} = \frac{3 π}{4}

\frac{\frac{3 π}{2}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{3 π}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{3 π}{4}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

= \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

csc (x) + 2 = 0 : x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

csc (x) + 2 = 0

Mover

2

al lado derecho

csc (x) + 2 = 0

Restar

2

de ambos lados

csc (x) + 2 - 2 = 0 - 2

Simplificar

csc (x) = - 2

csc (x) = - 2

Soluciones generales para

csc (x) = - 2

csc (x)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

csc (x) - 2 = 0 : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

csc (x) - 2 = 0

Mover

2

al lado derecho

csc (x) - 2 = 0

Sumar

2

a ambos lados

csc (x) - 2 + 2 = 0 + 2

Simplificar

csc (x) = 2

csc (x) = 2

Soluciones generales para

csc (x) = 2

csc (x)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

Combinar toda las soluciones

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

Mezclar intervalos sobrepuestos

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Ejemplos populares

2tan(x)sin(x)=sqrt(3)tan(x)

2 tan (x) sin (x) = 3 tan (x)

tan^3(2x)-tan^2(2x)-tan(2x)+1=0

tan^{3} (2 x) - tan^{2} (2 x) - tan (2 x) + 1 = 0

tan(x)=-sqrt(2)+1

tan (x) = - 2 + 1

sin(θ)= 12/20

sin (θ) = \frac{12}{20}

cos(x)=0.914

cos (x) = 0.914