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Popular >

2^{cot^2(x)}=8

Solución

2^{c o t^{2} (x)} = 8

Solución

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

+1

Grados

x = 3 0^{\circ} + 18 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n

Pasos de solución

2^{c o t^{2} (x)} = 8

Usando el método de sustitución

2^{c o t^{2} (x)} = 8

Sea:

cot (x) = u

2^{u^{2}} = 8

2^{u^{2}} = 8 : u = 3, u = - 3

2^{u^{2}} = 8

Aplicar las leyes de los exponentes

2^{u^{2}} = 8

Convertir a base

2 : 2^{u^{2}} = 2^{3}

Convertir

8

a base

2

8 = 2^{3}

2^{u^{2}} = 2^{3}

2^{u^{2}} = 2^{3}

Si

a^{f (x)} = a^{g (x)}

, entonces

f (x) = g (x)

u^{2} = 3

u^{2} = 3

Resolver

u^{2} = 3 : u = 3, u = - 3

u^{2} = 3

Para

x^{2} = f (a)

las soluciones son

x = f (a), - f (a)

u = 3, u = - 3

u = 3, u = - 3

Sustituir en la ecuación

u = cot (x)

cot (x) = 3, cot (x) = - 3

cot (x) = 3, cot (x) = - 3

cot (x) = 3 : x = \frac{π}{6} + πn

cot (x) = 3

Soluciones generales para

cot (x) = 3

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

cot (x) = - 3 : x = \frac{5 π}{6} + πn

cot (x) = - 3

Soluciones generales para

cot (x) = - 3

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

Combinar toda las soluciones

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Ejemplos populares

2*cos^2(x)+cos(x)-1=0

2 \cdot cos^{2} (x) + cos (x) - 1 = 0

cos (π y) = 0

cos (t) = - \frac{1}{3}

sqrt(3)cot(x)-1=0,0<= x<= 2pix

3 cot (x) - 1 = 0, 0 \leq x \leq 2 π x

1 = cosh (x)