Respuesta :
sex x = 1/cosx
tan x= sin x/cos x
sex x/tan x= (1/cosx) /(sin x/cos x) = (1/cosx) *(cos x/ sin x) = 1/sin x
Answer is 1/sin x or csc x.
[tex] \bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}
\qquad \qquad
csc(\theta)=\cfrac{1}{sin(\theta)}
\qquad \qquad
sec(\theta)=\cfrac{1}{cos(\theta)}\\\\
-------------------------------\\\\
\cfrac{sec(x)}{tan(x)}\implies \cfrac{\quad \frac{1}{cos(x)}\quad }{\frac{sin(x)}{cos(x)}}\implies \cfrac{1}{\underline{cos(x)}}\cdot \cfrac{\underline{cos(x)}}{sin(x)}\implies \cfrac{1}{sin(x)}\implies csc(x) [/tex]
