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cos(x)=(tan(x)+cot(x))/(csc(x))

Solución

cos (x) = \frac{tan ( x ) + cot ( x )}{csc ( x )}

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

Pasos de solución

cos (x) = \frac{tan ( x ) + cot ( x )}{csc ( x )}

Restar

\frac{tan ( x ) + cot ( x )}{csc ( x )}

de ambos lados

cos (x) - \frac{tan ( x ) + cot ( x )}{csc ( x )} = 0

Simplificar

cos (x) - \frac{tan ( x ) + cot ( x )}{csc ( x )} : \frac{cos ( x ) csc ( x ) - tan ( x ) - cot ( x )}{csc ( x )}

cos (x) - \frac{tan ( x ) + cot ( x )}{csc ( x )}

Convertir a fracción:

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

= \frac{cos ( x ) csc ( x )}{csc ( x )} - \frac{tan ( x ) + cot ( x )}{csc ( x )}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{cos ( x ) csc ( x ) - ( tan ( x ) + cot ( x ) )}{csc ( x )}

- (tan (x) + cot (x)) : - tan (x) - cot (x)

- (tan (x) + cot (x))

Poner los parentesis

= - (tan (x)) - (cot (x))

Aplicar las reglas de los signos

+ (- a) = - a

= - tan (x) - cot (x)

= \frac{cos ( x ) csc ( x ) - tan ( x ) - cot ( x )}{csc ( x )}

\frac{cos ( x ) csc ( x ) - tan ( x ) - cot ( x )}{csc ( x )} = 0

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

cos (x) csc (x) - tan (x) - cot (x) = 0

Re-escribir usando identidades trigonométricas

- cot (x) - tan (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)

= - cot (x) - tan (x) + cot (x)

Simplificar

= - tan (x)

- tan (x) = 0

Dividir ambos lados entre

- 1

- tan (x) = 0

Dividir ambos lados entre

- 1

\frac{- tan ( x )}{- 1} = \frac{0}{- 1}

Simplificar

tan (x) = 0

tan (x) = 0

Soluciones generales para

tan (x) = 0

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

Resolver

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

Siendo que la ecuación esta indefinida para:

πn

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

- tan^{2} (x) - 1 = 0

2 cot^{2} (y) + 3 csc (y) = 0

cot (x) = - 0.456

4 tan^{2} (θ) - 2 tan (θ) + 3 = - 7 tan (θ) + 2

- 2 = csc (θ)