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Popular >

tan(x)csc(x)-2tan(x)=3csc(x)-6

Solución

tan (x) csc (x) - 2 tan (x) = 3 csc (x) - 6

Solución

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = 1.24904 \dots + πn

+1

Grados

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n, x = 71.56505 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

tan (x) csc (x) - 2 tan (x) = 3 csc (x) - 6

Restar

3 csc (x) - 6

de ambos lados

tan (x) csc (x) - 2 tan (x) - 3 csc (x) + 6 = 0

Factorizar

tan (x) csc (x) - 2 tan (x) - 3 csc (x) + 6 : (csc (x) - 2) (tan (x) - 3)

tan (x) csc (x) - 2 tan (x) - 3 csc (x) + 6

= (tan (x) csc (x) - 2 tan (x)) + (- 3 csc (x) + 6)

Factorizar

- 3

de

- 3 csc (x) + 6

:

- 3 (csc (x) - 2)

- 3 csc (x) + 6

Reescribir

6

como

2 \cdot 3

= - 3 csc (x) + 2 \cdot 3

Factorizar el termino común

- 3

= - 3 (csc (x) - 2)

Factorizar

tan (x)

de

tan (x) csc (x) - 2 tan (x)

:

tan (x) (csc (x) - 2)

tan (x) csc (x) - 2 tan (x)

Factorizar el termino común

tan (x)

= tan (x) (csc (x) - 2)

= - 3 (csc (x) - 2) + tan (x) (csc (x) - 2)

Factorizar el termino común

csc (x) - 2

= (csc (x) - 2) (tan (x) - 3)

(csc (x) - 2) (tan (x) - 3) = 0

Resolver cada parte por separado

csc (x) - 2 = 0 or tan (x) - 3 = 0

csc (x) - 2 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 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}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

tan (x) - 3 = 0 : x = arctan (3) + πn

tan (x) - 3 = 0

Mover

3

al lado derecho

tan (x) - 3 = 0

Sumar

3

a ambos lados

tan (x) - 3 + 3 = 0 + 3

Simplificar

tan (x) = 3

tan (x) = 3

Aplicar propiedades trigonométricas inversas

tan (x) = 3

Soluciones generales para

tan (x) = 3

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (3) + πn

x = arctan (3) + πn

Combinar toda las soluciones

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = arctan (3) + πn

Mostrar soluciones en forma decimal

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = 1.24904 \dots + πn

Ejemplos populares

solvefor x,sin(x)=ln(y)resolver para

x, sin (x) = ln (y)

10=7cos((pi/6)(t+6))+8

10 = 7 cos ((\frac{π}{6}) (t + 6)) + 8

csc (t) = 2

cos(x)=-0.79497329

cos (x) = - 0.79497329

sin(x)+sin(x)=2

sin (x) + sin (x) = 2