Simplify tan x cot x

Step by step

The question

Question: simplify tan x × cot x.

Simplify means: write it as simply as we can.

1 Write in sin and cos

Everything is easier in sin and cos.

tan is sin over cos.

cot is cos over sin.

We put them in.

Tops go on top, bottoms at the bottom.

2 Cancel

Now we look for the same thing on top and at the bottom.

Careful!

sin x means the sine of x.

It is one thing.

We cross out a whole sin x, never the x alone.

Every sin x and cos x on top has a partner at the bottom.

Each pair over itself is 1.

Cross them out.

What is left: 1.

So it simplifies to 1.

3 Check

Let's check with a number: x = 30°.

On the calculator, tan 30° × cot 30° is about 1.0000.

Our answer is 1.

The same!

So it is right.

Let's look back.

First: write in sin and cos.

Then: cancel.

Last: check.