Simplify tan x cos x

Step by step

The question

Question: simplify tan x × cos 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.

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 cos x on top has a partner at the bottom.

Each pair over itself is 1.

Cross them out.

What is left: sin x.

So it simplifies to sin x.

3 Check

Let's check with a number: x = 30°.

On the calculator, tan 30° × cos 30° is about 0.5000.

And sin 30° is about 0.5000.

The same!

So it is right.

Let's look back.

First: write in sin and cos.

Then: cancel.

Last: check.