English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

6tan(x)(1-cos^2(x))=tan(x)

Solución

6 tan (x) (1 - cos^{2} (x)) = tan (x)

Solución

x = πn, x = 2.72105 \dots + 2 πn, x = - 2.72105 \dots + 2 πn, x = 0.42053 \dots + 2 πn, x = 2 π - 0.42053 \dots + 2 πn

Grados

x = 0^{\circ} + 18 0^{\circ} n, x = 155.90515 \dots^{\circ} + 36 0^{\circ} n, x = - 155.90515 \dots^{\circ} + 36 0^{\circ} n, x = 24.09484 \dots^{\circ} + 36 0^{\circ} n, x = 335.90515 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

6 tan (x) (1 - cos^{2} (x)) = tan (x)

Restar

tan (x)

de ambos lados

5 tan (x) - 6 cos^{2} (x) tan (x) = 0

Factorizar

5 tan (x) - 6 cos^{2} (x) tan (x) : - tan (x) (6 cos (x) + 5) (6 cos (x) - 5)

5 tan (x) - 6 cos^{2} (x) tan (x)

Factorizar el termino común

- tan (x)

= - tan (x) (- 5 + 6 cos^{2} (x))

Factorizar

6 cos^{2} (x) - 5 : (6 cos (x) + 5) (6 cos (x) - 5)

6 cos^{2} (x) - 5

Reescribir

6 cos^{2} (x) - 5

como

(6 cos (x))^{2} - (5)^{2}

6 cos^{2} (x) - 5

Aplicar las leyes de los exponentes:

a = (a)^{2}

6 = (6)^{2}

= (6)^{2} cos^{2} (x) - 5

Aplicar las leyes de los exponentes:

a = (a)^{2}

5 = (5)^{2}

= (6)^{2} cos^{2} (x) - (5)^{2}

Aplicar las leyes de los exponentes:

a^{m} b^{m} = (ab)^{m}

(6)^{2} cos^{2} (x) = (6 cos (x))^{2}

= (6 cos (x))^{2} - (5)^{2}

= (6 cos (x))^{2} - (5)^{2}

Aplicar la siguiente regla para binomios al cuadrado:

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

(6 cos (x))^{2} - (5)^{2} = (6 cos (x) + 5) (6 cos (x) - 5)

= (6 cos (x) + 5) (6 cos (x) - 5)

= - tan (x) (6 cos (x) + 5) (6 cos (x) - 5)

- tan (x) (6 cos (x) + 5) (6 cos (x) - 5) = 0

Resolver cada parte por separado

tan (x) = 0 or 6 cos (x) + 5 = 0 or 6 cos (x) - 5 = 0

tan (x) = 0 : x = πn

tan (x) = 0

Soluciones generales para

tan (x) = 0

tan (x)

tabla de valores periódicos con

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

Resolver

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

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

6 cos (x) + 5 = 0

Mover

5

al lado derecho

6 cos (x) + 5 = 0

Restar

5

de ambos lados

6 cos (x) + 5 - 5 = 0 - 5

Simplificar

6 cos (x) = - 5

6 cos (x) = - 5

Dividir ambos lados entre

6

6 cos (x) = - 5

Dividir ambos lados entre

6

\frac{6 cos ( x )}{6} = \frac{- 5}{6}

Simplificar

\frac{6 cos ( x )}{6} = \frac{- 5}{6}

Simplificar

\frac{6 cos ( x )}{6} : cos (x)

\frac{6 cos ( x )}{6}

Eliminar los terminos comunes:

6

= cos (x)

Simplificar

\frac{- 5}{6} : - \frac{5}{6}

\frac{- 5}{6}

Aplicar las propiedades de las fracciones:

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

= - \frac{5}{6}

Combinar los exponentes similares:

\frac{x}{y} = \frac{x}{y}

= - \frac{5}{6}

cos (x) = - \frac{5}{6}

cos (x) = - \frac{5}{6}

cos (x) = - \frac{5}{6}

Aplicar propiedades trigonométricas inversas

cos (x) = - \frac{5}{6}

Soluciones generales para

cos (x) = - \frac{5}{6}

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

x = arccos (- \frac{5}{6}) + 2 πn, x = - arccos (- \frac{5}{6}) + 2 πn

x = arccos (- \frac{5}{6}) + 2 πn, x = - arccos (- \frac{5}{6}) + 2 πn

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

6 cos (x) - 5 = 0

Mover

5

al lado derecho

6 cos (x) - 5 = 0

Sumar

5

a ambos lados

6 cos (x) - 5 + 5 = 0 + 5

Simplificar

6 cos (x) = 5

6 cos (x) = 5

Dividir ambos lados entre

6

6 cos (x) = 5

Dividir ambos lados entre

6

\frac{6 cos ( x )}{6} = \frac{5}{6}

Simplificar

\frac{6 cos ( x )}{6} = \frac{5}{6}

Simplificar

\frac{6 cos ( x )}{6} : cos (x)

\frac{6 cos ( x )}{6}

Eliminar los terminos comunes:

6

= cos (x)

Simplificar

\frac{5}{6} : \frac{5}{6}

\frac{5}{6}

Combinar los exponentes similares:

\frac{x}{y} = \frac{x}{y}

= \frac{5}{6}

cos (x) = \frac{5}{6}

cos (x) = \frac{5}{6}

cos (x) = \frac{5}{6}

Aplicar propiedades trigonométricas inversas

cos (x) = \frac{5}{6}

Soluciones generales para

cos (x) = \frac{5}{6}

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

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

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

Combinar toda las soluciones

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

Mostrar soluciones en forma decimal

x = πn, x = 2.72105 \dots + 2 πn, x = - 2.72105 \dots + 2 πn, x = 0.42053 \dots + 2 πn, x = 2 π - 0.42053 \dots + 2 πn

Ejemplos populares

cos^2(x)-sin^2(x)+sin(x)=1

cos^{2} (x) - sin^{2} (x) + sin (x) = 1

sin^3(x)-6sin^2(x)-sin(x)+6=0

sin^{3} (x) - 6 sin^{2} (x) - sin (x) + 6 = 0

tan(θ)= 8/(13.5)

tan (θ) = \frac{8}{13.5}

15sin(3x)=0

15 sin (3 x) = 0

sin(3θ)=-1,0<= θ<= 360

sin (3 θ) = - 1, 0^{\circ} \leq θ \leq 36 0^{\circ}