es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec(x)*cot(x)-2cot(x)+sec(x)=2

Solución

sec (x) \cdot cot (x) - 2 cot (x) + sec (x) = 2

Solución

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

+1

Grados

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

Pasos de solución

sec (x) cot (x) - 2 cot (x) + sec (x) = 2

Restar

2

de ambos lados

sec (x) cot (x) - 2 cot (x) + sec (x) - 2 = 0

Factorizar

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

sec (x) cot (x) - 2 cot (x) + sec (x) - 2

= (cot (x) sec (x) - 2 cot (x)) + (sec (x) - 2)

Factorizar

cot (x)

de

cot (x) sec (x) - 2 cot (x)

:

cot (x) (sec (x) - 2)

cot (x) sec (x) - 2 cot (x)

Factorizar el termino común

cot (x)

= cot (x) (sec (x) - 2)

= (sec (x) - 2) + cot (x) (sec (x) - 2)

Factorizar el termino común

sec (x) - 2

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

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

Resolver cada parte por separado

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

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

sec (x) - 2 = 0

Mover

2

al lado derecho

sec (x) - 2 = 0

Sumar

2

a ambos lados

sec (x) - 2 + 2 = 0 + 2

Simplificar

sec (x) = 2

sec (x) = 2

Soluciones generales para

sec (x) = 2

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

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

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

Combinar toda las soluciones

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

Ejemplos populares

3sin^2(x)-10sin(x)-8=0

3 sin^{2} (x) - 10 sin (x) - 8 = 0

2*9.8*L(1-cos(θ))=0.018

2 \cdot 9.8 \cdot L (1 - cos (θ)) = 0.018

cos(7x)=sin(4x+2)

cos (7 x) = sin (4 x + 2)

12cos(β)-5sin(β)=4.7

12 cos (β) - 5 sin (β) = 4.7

cos(x)=(sqrt(8))/3

cos (x) = \frac{8}{3}