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(sqrt(2))/2 csc(x)-1=0

Solución

\frac{2}{2} csc (x) - 1 = 0

Solución

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

+1

Grados

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

Pasos de solución

\frac{2}{2} csc (x) - 1 = 0

Multiplicar

\frac{2}{2} csc (x) : \frac{2 csc ( x )}{2}

\frac{2}{2} csc (x)

Multiplicar fracciones:

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

= \frac{2 csc ( x )}{2}

\frac{2 csc ( x )}{2} - 1 = 0

Mover

1

al lado derecho

\frac{2 csc ( x )}{2} - 1 = 0

Sumar

1

a ambos lados

\frac{2 csc ( x )}{2} - 1 + 1 = 0 + 1

Simplificar

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

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

Multiplicar ambos lados por

2

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

Multiplicar ambos lados por

2

\frac{2 2 csc ( x )}{2} = 1 \cdot 2

Simplificar

2 csc (x) = 2

2 csc (x) = 2

Dividir ambos lados entre

2

2 csc (x) = 2

Dividir ambos lados entre

2

\frac{2 csc ( x )}{2} = \frac{2}{2}

Simplificar

\frac{2 csc ( x )}{2} = \frac{2}{2}

Simplificar

\frac{2 csc ( x )}{2} : csc (x)

\frac{2 csc ( x )}{2}

Eliminar los terminos comunes:

2

= csc (x)

Simplificar

\frac{2}{2} : 2

\frac{2}{2}

Aplicar las leyes de los exponentes:

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

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

Aplicar las leyes de los exponentes:

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

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

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

Restar:

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

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

Aplicar las leyes de los exponentes:

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

= 2

csc (x) = 2

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

Ejemplos populares

cos(3x)cos(x)=sin(3x)sin(x)

cos (3 x) cos (x) = sin (3 x) sin (x)

2sin(x)cos(x)+cos(x)=0

2 sin (x) cos (x) + cos (x) = 0

2 cos (4 x) - 1 = 0

cot(x)=(sqrt(3))/3

cot (x) = \frac{3}{3}

sin^2(x)=1,0<= x<= 2pi

sin^{2} (x) = 1, 0 \leq x \leq 2 π