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Popular >

cot(x)+csc(x)cos(x)=2,cot(x)

Solución

cot (x) + csc (x) cos (x) = 2, cot (x)

Solución

Sin soluci \overset{o}{ˊ} n para x \in R

Pasos de solución

cot (x) + csc (x) cos (x) = 2, cot (x)

Restar

2

de ambos lados

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

Re-escribir usando identidades trigonométricas

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

csc (x) cos (x) = cot (x)

csc (x) cos (x)

Expresar con seno, coseno

csc (x) cos (x)

Utilizar la identidad trigonométrica básica:

csc (x) = \frac{1}{sin ( x )}

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

Simplificar

\frac{1}{sin ( x )} cos (x) : \frac{cos ( x )}{sin ( x )}

\frac{1}{sin ( x )} cos (x)

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Multiplicar:

1 \cdot cos (x) = cos (x)

= \frac{cos ( x )}{sin ( x )}

= \frac{cos ( x )}{sin ( x )}

= \frac{cos ( x )}{sin ( x )}

Utilizar la identidad trigonométrica básica:

\frac{cos ( x )}{sin ( x )} = cot (x)

= cot (x)

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

Simplificar

= - 2 + 2 cot (x)

- 2 + 2 cot (x) = 0

Mover

2

al lado derecho

- 2 + 2 cot (x) = 0

Sumar

2

a ambos lados

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

Simplificar

2 cot (x) = 2

2 cot (x) = 2

Dividir ambos lados entre

2

2 cot (x) = 2

Dividir ambos lados entre

2

\frac{2 cot ( x )}{2} = \frac{2}{2}

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{π}{4} + πn

x = \frac{π}{4} + πn

Soluciones para el rango

cot (x)

Sin soluci \overset{o}{ˊ} n para x \in R

Ejemplos populares

- 4 cos (3 θ) = 1

960=480(1-cos(7.5x))

960 = 480 (1 - cos (7.5 x))

8 = 8 tan (θ)

2sin(2x)-3cos(x)=0

2 sin (2 x) - 3 cos (x) = 0

4cos(θ)=2cos(θ)

4 cos (θ) = 2 cos (θ)