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tan(2x-pi/6)= 1/(3^{1/2)}

Solución

tan (2 x - \frac{π}{6}) = \frac{1}{3 ^{\frac{1}{2}}}

Solución

x = \frac{π}{6} + \frac{πn}{2}

Grados

x = 3 0^{\circ} + 9 0^{\circ} n

Pasos de solución

tan (2 x - \frac{π}{6}) = \frac{1}{3 ^{\frac{1}{2}}}

Aplicar propiedades trigonométricas inversas

tan (2 x - \frac{π}{6}) = \frac{1}{3 ^{\frac{1}{2}}}

Soluciones generales para

tan (2 x - \frac{π}{6}) = \frac{1}{3 ^{\frac{1}{2}}}

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

2 x - \frac{π}{6} = arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn

2 x - \frac{π}{6} = arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn

Resolver

2 x - \frac{π}{6} = arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn : x = \frac{π}{6} + \frac{πn}{2}

2 x - \frac{π}{6} = arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn

Simplificar

arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn : \frac{π}{6} + πn

arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn

Utilizar la siguiente identidad trivial:

arctan (\frac{1}{3 ^{\frac{1}{2}}}) = \frac{π}{6}

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{6} + πn

2 x - \frac{π}{6} = \frac{π}{6} + πn

Mover

\frac{π}{6}

al lado derecho

2 x - \frac{π}{6} = \frac{π}{6} + πn

Sumar

\frac{π}{6}

a ambos lados

2 x - \frac{π}{6} + \frac{π}{6} = \frac{π}{6} + πn + \frac{π}{6}

Simplificar

2 x - \frac{π}{6} + \frac{π}{6} = \frac{π}{6} + πn + \frac{π}{6}

Simplificar

2 x - \frac{π}{6} + \frac{π}{6} : 2 x

2 x - \frac{π}{6} + \frac{π}{6}

Sumar elementos similares:

- \frac{π}{6} + \frac{π}{6} = 0

= 2 x

Simplificar

\frac{π}{6} + πn + \frac{π}{6} : \frac{π}{3} + πn

\frac{π}{6} + πn + \frac{π}{6}

Agrupar términos semejantes

= \frac{π}{6} + \frac{π}{6} + πn

Combinar las fracciones usando el mínimo común denominador:

\frac{π}{3}

Aplicar la regla

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

= \frac{π + π}{6}

Sumar elementos similares:

π + π = 2 π

= \frac{2 π}{6}

Eliminar los terminos comunes:

2

= \frac{π}{3}

= \frac{π}{3} + πn

2 x = \frac{π}{3} + πn

2 x = \frac{π}{3} + πn

2 x = \frac{π}{3} + πn

Dividir ambos lados entre

2

2 x = \frac{π}{3} + πn

Dividir ambos lados entre

2

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

Simplificar

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

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{\frac{π}{3}}{2} + \frac{πn}{2} : \frac{π}{6} + \frac{πn}{2}

\frac{\frac{π}{3}}{2} + \frac{πn}{2}

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{3 \cdot 2}

Multiplicar los numeros:

3 \cdot 2 = 6

= \frac{π}{6}

= \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

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