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Popular >

solvefor 3cot^2(x)-1=0,x

Solución

resolver para

3 cot^{2} (x) - 1 = 0, x

Solución

x = 1.04719 \dots + πn, x = 2.09439 \dots + πn

+1

Grados

x = 6 0^{\circ} + 18 0^{\circ} n, x = 12 0^{\circ} + 18 0^{\circ} n

Pasos de solución

3 cot^{2} (x) - 1 = 0

Usando el método de sustitución

3 cot^{2} (x) - 1 = 0

Sea:

cot (x) = u

3 u^{2} - 1 = 0

3 u^{2} - 1 = 0 : u = \frac{1}{3}, u = - \frac{1}{3}

3 u^{2} - 1 = 0

Mover

1

al lado derecho

3 u^{2} - 1 = 0

Sumar

1

a ambos lados

3 u^{2} - 1 + 1 = 0 + 1

Simplificar

3 u^{2} = 1

3 u^{2} = 1

Dividir ambos lados entre

3

3 u^{2} = 1

Dividir ambos lados entre

3

\frac{3 u ^{2}}{3} = \frac{1}{3}

Simplificar

u^{2} = \frac{1}{3}

u^{2} = \frac{1}{3}

Para

x^{2} = f (a)

las soluciones son

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

u = \frac{1}{3}, u = - \frac{1}{3}

Sustituir en la ecuación

u = cot (x)

cot (x) = \frac{1}{3}, cot (x) = - \frac{1}{3}

cot (x) = \frac{1}{3}, cot (x) = - \frac{1}{3}

cot (x) = \frac{1}{3} : x = arccot (\frac{1}{3}) + πn

cot (x) = \frac{1}{3}

Aplicar propiedades trigonométricas inversas

cot (x) = \frac{1}{3}

Soluciones generales para

cot (x) = \frac{1}{3}

cot (x) = a \Rightarrow x = arccot (a) + πn

x = arccot (\frac{1}{3}) + πn

x = arccot (\frac{1}{3}) + πn

cot (x) = - \frac{1}{3} : x = arccot (- \frac{1}{3}) + πn

cot (x) = - \frac{1}{3}

Aplicar propiedades trigonométricas inversas

cot (x) = - \frac{1}{3}

Soluciones generales para

cot (x) = - \frac{1}{3}

cot (x) = - a \Rightarrow x = arccot (- a) + πn

x = arccot (- \frac{1}{3}) + πn

x = arccot (- \frac{1}{3}) + πn

Combinar toda las soluciones

x = arccot (\frac{1}{3}) + πn, x = arccot (- \frac{1}{3}) + πn

Mostrar soluciones en forma decimal

x = 1.04719 \dots + πn, x = 2.09439 \dots + πn

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tan (a) = \frac{2.8}{9}

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