We have an answer to "How do you simplify sec⁡xtan⁡x?"

regatamin2

Answered question

2021-12-13

How do you simplify

\frac{\sec x}{\tan x}

Bertha Jordan

Beginner2021-12-14Added 37 answers

Use

\tan x = \frac{\sin x}{\cos x}

And

\sec x = \frac{1}{\cos x}

So,

\frac{\sec x}{\tan x} = \frac{1}{\cos x} \cdot \frac{\cos x}{\sin x} = \frac{1}{\sin x} = \csc x

Navreaiw

Beginner2021-12-15Added 34 answers

Let's use the definitions of

\sec x

and

\tan x

to simplify this. We know

\sec x = \frac{1}{\cos x}

and

\tan x = \frac{\sin x}{\cos x}

. Let's plug these values into our original expression. we get

\frac{\frac{1}{\cos x}}{\frac{\sin x}{\cos x}} = \frac{1}{\sin x} \Rightarrow \csc x

Therefore,

\frac{\sec x}{\tan x} = \csc x

Hope this helps!

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