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Popular >

csc(x)+cot(x)=0

Solución

csc (x) + cot (x) = 0

Solución

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

Pasos de solución

csc (x) + cot (x) = 0

Expresar con seno, coseno

cot (x) + csc (x)

Utilizar la identidad trigonométrica básica:

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

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

Utilizar la identidad trigonométrica básica:

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

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

Simplificar

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

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

Aplicar la regla

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

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

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

\frac{1 + cos ( x )}{sin ( x )} = 0

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

1 + cos (x) = 0

Mover

1

al lado derecho

1 + cos (x) = 0

Restar

1

de ambos lados

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

Simplificar

cos (x) = - 1

cos (x) = - 1

Soluciones generales para

cos (x) = - 1

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 = π + 2 πn

x = π + 2 πn

Siendo que la ecuación esta indefinida para:

π + 2 πn

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

Gráfica

Ejemplos populares

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