Simplify cos x csc x

Step by step

The question

Question: simplify cos x × csc x.

Simplify means: write it as simply as we can.

1 Write in sin and cos

Everything is easier in sin and cos.

csc is 1 over sin.

We put them in.

Tops go on top, bottoms at the bottom.

2 Name it

cos x over sin x has its own name: cot x.

So it simplifies to cot x.

3 Check

Let's check with a number: x = 30°.

On the calculator, cos 30° × csc 30° is about 1.7321.

And cot 30° is about 1.7321.

The same!

So it is right.

Let's look back.

First: write in sin and cos.

Then: name it.

Last: check.