Question

Simply the expression (Picture provided)

Answer 1

Answer:

b. $\csc(x)$

Step-by-step explanation:

The given expression is

$\frac{\sec(x)}{\tan(x)}$

We express in terms of basic trigonometric ratios to obtain;

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

This is the same as

$\frac{1}{\cos(x)}\div \frac{\sin(x)}{\cos(x)}$

$\frac{1}{\cos(x)}\times \frac{\cos(x)}{\sin(x)}$

Cancel out the common factors;

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

Answer 2

Answer:

$\frac{secx}{tanx}$  = cscx

Step-by-step explanation:

We have given a trigonometric expression.

$\frac{secx}{tanx}$

We have to simplify the above expression.

Since, we know that

secx is reciprocal of cosx.

secx  =  1/cosx

Tanx is the ratio of sinx and cosx.

Tanx  =  sinx / cosx

Given expression becomes

$\frac{1/cosx}{sinx/cosx}$

$\frac{1}{cosx}\frac{cosx}{sinx}$

$\frac{1}{sinx}$

$\frac{secx}{tanx}$  = cscx which is the answer.