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 )}

\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

- tan (x) = 0

Dividir ambos lados entre

- 1

tan (x) = 0

Soluciones generales para

tan (x) = 0

x = 0 + πn

Resolver

x = 0 + 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)