Simplify cot x sin x

Step by step

The question

Question: simplify cot x × sin x.

Simplify means: write it as simply as we can.

1 Write in sin and cos

Everything is easier in sin and 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 on top has a partner at the bottom.

Each pair over itself is 1.

Cross them out.

What is left: cos x.

So it simplifies to cos x.

3 Check

Let's check with a number: x = 30°.

On the calculator, cot 30° × sin 30° is about 0.8660.

And cos 30° is about 0.8660.

The same!

So it is right.

Let's look back.

First: write in sin and cos.

Then: cancel.

Last: check.