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2csc(x)+7/(cos(x))=0

Solución

2 csc (x) + \frac{7}{cos ( x )} = 0

x = 2.86329 \dots + πn

Grados

x = 164.05460 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

2 csc (x) + \frac{7}{cos ( x )} = 0

Simplificar

2 csc (x) + \frac{7}{cos ( x )} : \frac{2 csc ( x ) cos ( x ) + 7}{cos ( x )}

2 csc (x) + \frac{7}{cos ( x )}

Convertir a fracción:

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

= \frac{2 csc ( x ) cos ( x )}{cos ( x )} + \frac{7}{cos ( x )}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{2 csc ( x ) cos ( x ) + 7}{cos ( x )}

\frac{2 csc ( x ) cos ( x ) + 7}{cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 csc (x) cos (x) + 7 = 0

Re-escribir usando identidades trigonométricas

2 csc (x) cos (x) + 7

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)

= 7 + 2 cot (x)

7 + 2 cot (x) = 0

Mover

7

al lado derecho

7 + 2 cot (x) = 0

Restar

7

de ambos lados

7 + 2 cot (x) - 7 = 0 - 7

Simplificar

2 cot (x) = - 7

2 cot (x) = - 7

Dividir ambos lados entre

2

2 cot (x) = - 7

Dividir ambos lados entre

2

\frac{2 cot ( x )}{2} = \frac{- 7}{2}

Simplificar

cot (x) = - \frac{7}{2}

cot (x) = - \frac{7}{2}

Aplicar propiedades trigonométricas inversas

cot (x) = - \frac{7}{2}

Soluciones generales para

cot (x) = - \frac{7}{2}

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

x = arccot (- \frac{7}{2}) + πn

x = arccot (- \frac{7}{2}) + πn

Mostrar soluciones en forma decimal

x = 2.86329 \dots + πn

csc (θ) = \frac{13}{6}

tan (B) = 8

\frac{tan ( θ ) cot ( θ )}{sec ^{2} ( θ )} = cot (θ)

3 - 3 cot (x) = - 6 cot (x)

sin (y) = \frac{3}{2}