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Popular >

cot(x)cos^2(x)=cot(x)

Solución

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

Solución

x = \frac{π}{2} + πn

Grados

x = 9 0^{\circ} + 18 0^{\circ} n

Pasos de solución

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

Restar

cot (x)

de ambos lados

cos^{2} (x) cot (x) - cot (x) = 0

Factorizar

cos^{2} (x) cot (x) - cot (x) : cot (x) (cos (x) + 1) (cos (x) - 1)

cos^{2} (x) cot (x) - cot (x)

Factorizar el termino común

cot (x)

= cot (x) (cos^{2} (x) - 1)

Factorizar

cos^{2} (x) - 1 : (cos (x) + 1) (cos (x) - 1)

cos^{2} (x) - 1

Reescribir

1

como

1^{2}

= cos^{2} (x) - 1^{2}

Aplicar la siguiente regla para binomios al cuadrado:

x^{2} - y^{2} = (x + y) (x - y)

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

= (cos (x) + 1) (cos (x) - 1)

= cot (x) (cos (x) + 1) (cos (x) - 1)

cot (x) (cos (x) + 1) (cos (x) - 1) = 0

Resolver cada parte por separado

cot (x) = 0 or cos (x) + 1 = 0 or cos (x) - 1 = 0

cot (x) = 0 : x = \frac{π}{2} + πn

cot (x) = 0

Soluciones generales para

cot (x) = 0

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}{2} + πn

x = \frac{π}{2} + πn

cos (x) + 1 = 0 : x = π + 2 πn

cos (x) + 1 = 0

Mover

1

al lado derecho

cos (x) + 1 = 0

Restar

1

de ambos lados

cos (x) + 1 - 1 = 0 - 1

Simplificar

cos (x) = - 1

cos (x) = - 1

Soluciones generales para

cos (x) = - 1

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}

x = π + 2 πn

x = π + 2 πn

cos (x) - 1 = 0 : x = 2 πn

cos (x) - 1 = 0

Mover

1

al lado derecho

cos (x) - 1 = 0

Sumar

1

a ambos lados

cos (x) - 1 + 1 = 0 + 1

Simplificar

cos (x) = 1

cos (x) = 1

Soluciones generales para

cos (x) = 1

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}

x = 0 + 2 πn

x = 0 + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

Combinar toda las soluciones

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

Siendo que la ecuación esta indefinida para:

π + 2 πn, 2 πn

x = \frac{π}{2} + πn

Ejemplos populares

2sin(2x)+5=4

2 sin (2 x) + 5 = 4

solvefor x,sin(x)=cos(x)resolver para

x, sin (x) = cos (x)

sin(θ)=-(sqrt(3))/2 ,0<= θ<= 2pi

sin (θ) = - \frac{3}{2}, 0 \leq θ \leq 2 π

sin(x)+cos(x)= 1/(sqrt(2))

sin (x) + cos (x) = \frac{1}{2}

cot(x)=4

cot (x) = 4