Question

Simplify the expression (sec x/ tan x)

Answer 1

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.

Answer 2

$\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \qquad \qquad csc(\theta)=\cfrac{1}{sin(\theta)} \qquad \qquad sec(\theta)=\cfrac{1}{cos(\theta)}\\\\ -------------------------------\\\\ \cfrac{sec(x)}{tan(x)}\implies \cfrac{\quad \frac{1}{cos(x)}\quad }{\frac{sin(x)}{cos(x)}}\implies \cfrac{1}{\underline{cos(x)}}\cdot \cfrac{\underline{cos(x)}}{sin(x)}\implies \cfrac{1}{sin(x)}\implies csc(x)$