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Popular >

(2*40)/(80+20)=tan(2x)

Solución

\frac{2 \cdot 40}{80 + 20} = tan (2 x)

Solución

x = \frac{0.67474 \dots}{2} + \frac{πn}{2}

+1

Grados

x = 19.32990 \dots^{\circ} + 9 0^{\circ} n

Pasos de solución

\frac{2 \cdot 40}{80 + 20} = tan (2 x)

Intercambiar lados

tan (2 x) = \frac{2 \cdot 40}{80 + 20}

Simplificar

\frac{2 \cdot 40}{80 + 20} : \frac{4}{5}

\frac{2 \cdot 40}{80 + 20}

Multiplicar los numeros:

2 \cdot 40 = 80

= \frac{80}{80 + 20}

Sumar:

80 + 20 = 100

= \frac{80}{100}

Eliminar los terminos comunes:

20

= \frac{4}{5}

Aplicar propiedades trigonométricas inversas

tan (2 x) = \frac{4}{5}

Soluciones generales para

tan (2 x) = \frac{4}{5}

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

2 x = arctan (\frac{4}{5}) + πn

2 x = arctan (\frac{4}{5}) + πn

Resolver

2 x = arctan (\frac{4}{5}) + πn : x = \frac{arctan ( \frac{4}{5} )}{2} + \frac{πn}{2}

2 x = arctan (\frac{4}{5}) + πn

Dividir ambos lados entre

2

2 x = arctan (\frac{4}{5}) + πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arctan ( \frac{4}{5} )}{2} + \frac{πn}{2}

Simplificar

x = \frac{arctan ( \frac{4}{5} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{4}{5} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{4}{5} )}{2} + \frac{πn}{2}

Mostrar soluciones en forma decimal

x = \frac{0.67474 \dots}{2} + \frac{πn}{2}

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