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tan(2x)=(((300))/(200-(-400))*2)

Solución

tan (2 x) = (\frac{( 300 )}{200 - ( - 400 )} \cdot 2)

x = \frac{π}{8} + \frac{πn}{2}

radianes

x = \frac{π}{8} + \frac{π}{2} n

Pasos de solución

tan (2 x) = (\frac{( 300 )}{200 - ( - 400 )} \cdot 2)

Simplificar

\frac{300}{200 - ( - 400 )} \cdot 2 : 1

\frac{300}{200 - ( - 400 )} \cdot 2

Aplicar la regla

- (- a) = a

= \frac{300}{200 + 400} \cdot 2

\frac{300}{200 + 400} = \frac{1}{2}

\frac{300}{200 + 400}

Sumar:

200 + 400 = 600

= \frac{300}{600}

Eliminar los terminos comunes:

300

= \frac{1}{2}

= 2 \cdot \frac{1}{2}

Multiplicar fracciones:

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

= \frac{1 \cdot 2}{2}

Eliminar los terminos comunes:

2

= 1

Soluciones generales para

tan (2 x) = 1

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}

2 x = \frac{π}{4} + πn

2 x = \frac{π}{4} + πn

Resolver

2 x = \frac{π}{4} + πn : x = \frac{π}{8} + \frac{πn}{2}

2 x = \frac{π}{4} + πn

Dividir ambos lados entre

2

2 x = \frac{π}{4} + πn

Dividir ambos lados entre

2

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

Simplificar

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

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{\frac{π}{4}}{2} + \frac{πn}{2} : \frac{π}{8} + \frac{πn}{2}

\frac{\frac{π}{4}}{2} + \frac{πn}{2}

\frac{\frac{π}{4}}{2} = \frac{π}{8}

\frac{\frac{π}{4}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{4 \cdot 2}

Multiplicar los numeros:

4 \cdot 2 = 8

= \frac{π}{8}

= \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

cos (2 x) = 0.37

15 cot^{2} (x) = 5

cos (2 x) - sin (x) = 1, 0 \leq x < 2 π

sec^{2} (x) + 5 sec (x) - 14 = 0

3 cos^{2} (x) = 1