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Popular >

5cos(x)cot(x)-3cos(x)-10cot(x)+6=0

Solución

5 cos (x) cot (x) - 3 cos (x) - 10 cot (x) + 6 = 0

Solución

x = 1.03037 \dots + πn

+1

Grados

x = 59.03624 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

5 cos (x) cot (x) - 3 cos (x) - 10 cot (x) + 6 = 0

Factorizar

5 cos (x) cot (x) - 3 cos (x) - 10 cot (x) + 6 : (5 cot (x) - 3) (cos (x) - 2)

5 cos (x) cot (x) - 3 cos (x) - 10 cot (x) + 6

= (5 cot (x) cos (x) - 3 cos (x)) + (- 10 cot (x) + 6)

Factorizar

- 2

de

- 10 cot (x) + 6

:

- 2 (5 cot (x) - 3)

- 10 cot (x) + 6

Reescribir

6

como

3 \cdot 2

Reescribir

- 10

como

5 \cdot 2

= 5 \cdot 2 cot (x) + 3 \cdot 2

Factorizar el termino común

- 2

= - 2 (5 cot (x) - 3)

Factorizar

cos (x)

de

5 cot (x) cos (x) - 3 cos (x)

:

cos (x) (5 cot (x) - 3)

5 cot (x) cos (x) - 3 cos (x)

Factorizar el termino común

cos (x)

= cos (x) (5 cot (x) - 3)

= - 2 (5 cot (x) - 3) + cos (x) (5 cot (x) - 3)

Factorizar el termino común

5 cot (x) - 3

= (5 cot (x) - 3) (cos (x) - 2)

(5 cot (x) - 3) (cos (x) - 2) = 0

Resolver cada parte por separado

5 cot (x) - 3 = 0 or cos (x) - 2 = 0

5 cot (x) - 3 = 0 : x = arccot (\frac{3}{5}) + πn

5 cot (x) - 3 = 0

Mover

3

al lado derecho

5 cot (x) - 3 = 0

Sumar

3

a ambos lados

5 cot (x) - 3 + 3 = 0 + 3

Simplificar

5 cot (x) = 3

5 cot (x) = 3

Dividir ambos lados entre

5

5 cot (x) = 3

Dividir ambos lados entre

5

\frac{5 cot ( x )}{5} = \frac{3}{5}

Simplificar

cot (x) = \frac{3}{5}

cot (x) = \frac{3}{5}

Aplicar propiedades trigonométricas inversas

cot (x) = \frac{3}{5}

Soluciones generales para

cot (x) = \frac{3}{5}

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

x = arccot (\frac{3}{5}) + πn

x = arccot (\frac{3}{5}) + πn

cos (x) - 2 = 0 :

Sin solución

cos (x) - 2 = 0

Mover

2

al lado derecho

cos (x) - 2 = 0

Sumar

2

a ambos lados

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

Simplificar

cos (x) = 2

cos (x) = 2

- 1 \leq cos (x) \leq 1

Sin soluci \overset{o}{ˊ} n

Combinar toda las soluciones

x = arccot (\frac{3}{5}) + πn

Mostrar soluciones en forma decimal

x = 1.03037 \dots + πn

Ejemplos populares

cos(x)=(-1)/(sqrt(2))

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

sin^2(x)=cos^2(x)-sin(x)

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

solvefor y,cos(y)=x resolver para

y, cos (y) = x

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

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

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

1 + sin (x) = cos (x)