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Popular >

sin(2x)sin(4x)=cos(2x)cos(4x)

Solución

sin (2 x) sin (4 x) = cos (2 x) cos (4 x)

Solución

x = \frac{π}{12} + \frac{πn}{3}, x = \frac{π}{4} + \frac{πn}{3}

Grados

x = 1 5^{\circ} + 6 0^{\circ} n, x = 4 5^{\circ} + 6 0^{\circ} n

Pasos de solución

sin (2 x) sin (4 x) = cos (2 x) cos (4 x)

Restar

cos (2 x) cos (4 x)

de ambos lados

sin (2 x) sin (4 x) - cos (2 x) cos (4 x) = 0

Re-escribir usando identidades trigonométricas

sin (2 x) sin (4 x) - cos (2 x) cos (4 x)

Utilizar la identidad de suma de ángulos:

cos (s) cos (t) - sin (s) sin (t) = cos (s + t)

- cos (s) cos (t) + sin (s) sin (t) = - cos (s + t)

= - cos (2 x + 4 x)

- cos (2 x + 4 x) = 0

Dividir ambos lados entre

- 1

- cos (2 x + 4 x) = 0

Dividir ambos lados entre

- 1

\frac{- cos ( 2 x + 4 x )}{- 1} = \frac{0}{- 1}

Simplificar

cos (2 x + 4 x) = 0

cos (2 x + 4 x) = 0

Soluciones generales para

cos (2 x + 4 x) = 0

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

2 x + 4 x = \frac{π}{2} + 2 πn, 2 x + 4 x = \frac{3 π}{2} + 2 πn

2 x + 4 x = \frac{π}{2} + 2 πn, 2 x + 4 x = \frac{3 π}{2} + 2 πn

Resolver

2 x + 4 x = \frac{π}{2} + 2 πn : x = \frac{π}{12} + \frac{πn}{3}

2 x + 4 x = \frac{π}{2} + 2 πn

Sumar elementos similares:

2 x + 4 x = 6 x

6 x = \frac{π}{2} + 2 πn

Dividir ambos lados entre

6

6 x = \frac{π}{2} + 2 πn

Dividir ambos lados entre

6

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

Simplificar

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

Simplificar

\frac{6 x}{6} : x

\frac{6 x}{6}

Dividir:

\frac{6}{6} = 1

= x

Simplificar

\frac{\frac{π}{2}}{6} + \frac{2 πn}{6} : \frac{π}{12} + \frac{πn}{3}

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

\frac{\frac{π}{2}}{6} = \frac{π}{12}

\frac{\frac{π}{2}}{6}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{2 \cdot 6}

Multiplicar los numeros:

2 \cdot 6 = 12

= \frac{π}{12}

\frac{2 πn}{6} = \frac{πn}{3}

\frac{2 πn}{6}

Eliminar los terminos comunes:

2

= \frac{πn}{3}

= \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

Resolver

2 x + 4 x = \frac{3 π}{2} + 2 πn : x = \frac{π}{4} + \frac{πn}{3}

2 x + 4 x = \frac{3 π}{2} + 2 πn

Sumar elementos similares:

2 x + 4 x = 6 x

6 x = \frac{3 π}{2} + 2 πn

Dividir ambos lados entre

6

6 x = \frac{3 π}{2} + 2 πn

Dividir ambos lados entre

6

\frac{6 x}{6} = \frac{\frac{3 π}{2}}{6} + \frac{2 πn}{6}

Simplificar

\frac{6 x}{6} = \frac{\frac{3 π}{2}}{6} + \frac{2 πn}{6}

Simplificar

\frac{6 x}{6} : x

\frac{6 x}{6}

Dividir:

\frac{6}{6} = 1

= x

Simplificar

\frac{\frac{3 π}{2}}{6} + \frac{2 πn}{6} : \frac{π}{4} + \frac{πn}{3}

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

\frac{\frac{3 π}{2}}{6} = \frac{π}{4}

\frac{\frac{3 π}{2}}{6}

Aplicar las propiedades de las fracciones:

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

= \frac{3 π}{2 \cdot 6}

Multiplicar los numeros:

2 \cdot 6 = 12

= \frac{3 π}{12}

Eliminar los terminos comunes:

3

= \frac{π}{4}

\frac{2 πn}{6} = \frac{πn}{3}

\frac{2 πn}{6}

Eliminar los terminos comunes:

2

= \frac{πn}{3}

= \frac{π}{4} + \frac{πn}{3}

x = \frac{π}{4} + \frac{πn}{3}

x = \frac{π}{4} + \frac{πn}{3}

x = \frac{π}{4} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}, x = \frac{π}{4} + \frac{πn}{3}

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solvefor x,2sin(5x)-1=0 resolver para

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2*cos(2x)+1=0

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