Question

Simply the expression (Picture provided)

Answer 1

`(secx)/(tanx)` = cscx

Explanation:

We have given a trigonometric expression.

`(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

`(1/cosx)/(sinx/cosx)`

`(1)/(cosx)(cosx)/(sinx)`

`(1)/(sinx)`

`(secx)/(tanx)` = cscx which is the answer.

Answer 2

b.
`\csc(x)`

Explanation:

The given expression is

`(\sec(x))/(\tan(x))`

We express in terms of basic trigonometric ratios to obtain;

`((1)/(\cos(x)) )/((\sin(x))/(\cos(x)) )`

This is the same as

`(1)/(\cos(x))/ (\sin(x))/(\cos(x))`

`(1)/(\cos(x))* (\cos(x))/(\sin(x))`

Cancel out the common factors;

`(1)/(\sin(x))=\csc(x)`