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Popular >

2cot(x)cos(x)+2cos(x)=cot(x)+1

Solución

2 cot (x) cos (x) + 2 cos (x) = cot (x) + 1

Solución

x = \frac{3 π}{4} + πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

Grados

x = 13 5^{\circ} + 18 0^{\circ} n, x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Pasos de solución

2 cot (x) cos (x) + 2 cos (x) = cot (x) + 1

Restar

cot (x) + 1

de ambos lados

2 cot (x) cos (x) + 2 cos (x) - cot (x) - 1 = 0

Factorizar

2 cot (x) cos (x) + 2 cos (x) - cot (x) - 1 : (cot (x) + 1) (2 cos (x) - 1)

2 cot (x) cos (x) + 2 cos (x) - cot (x) - 1

= (2 cot (x) cos (x) + 2 cos (x)) + (- cot (x) - 1)

Factorizar

- 1

de

- cot (x) - 1

:

- (cot (x) + 1)

- cot (x) - 1

Factorizar el termino común

- 1

= - (cot (x) + 1)

Factorizar

2 cos (x)

de

2 cot (x) cos (x) + 2 cos (x)

:

2 cos (x) (cot (x) + 1)

2 cot (x) cos (x) + 2 cos (x)

Factorizar el termino común

2 cos (x)

= 2 cos (x) (cot (x) + 1)

= - (cot (x) + 1) + 2 cos (x) (cot (x) + 1)

Factorizar el termino común

cot (x) + 1

= (cot (x) + 1) (2 cos (x) - 1)

(cot (x) + 1) (2 cos (x) - 1) = 0

Resolver cada parte por separado

cot (x) + 1 = 0 or 2 cos (x) - 1 = 0

cot (x) + 1 = 0 : x = \frac{3 π}{4} + πn

cot (x) + 1 = 0

Mover

1

al lado derecho

cot (x) + 1 = 0

Restar

1

de ambos lados

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

Simplificar

cot (x) = - 1

cot (x) = - 1

Soluciones generales para

cot (x) = - 1

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{3 π}{4} + πn

x = \frac{3 π}{4} + πn

2 cos (x) - 1 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 cos (x) - 1 = 0

Mover

1

al lado derecho

2 cos (x) - 1 = 0

Sumar

1

a ambos lados

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

Simplificar

2 cos (x) = 1

2 cos (x) = 1

Dividir ambos lados entre

2

2 cos (x) = 1

Dividir ambos lados entre

2

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

Simplificar

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

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

Soluciones generales para

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

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 = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combinar toda las soluciones

x = \frac{3 π}{4} + πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Ejemplos populares

tan(θ)-7=-12cot(θ)

tan (θ) - 7 = - 12 cot (θ)

2*sin^2(x)-sin(x)=1

2 \cdot sin^{2} (x) - sin (x) = 1

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

6sin(b)+sqrt(12)=0

6 sin (b) + 12 = 0

40+40cos((2pix)/9)=50

40 + 40 cos (\frac{2 π x}{9}) = 50