Simplify sin x cos x / sin^2 x

Step by step

The question

Question: simplify sin x × cos x over sin² x.

Simplify means: write it as simply as we can.

1 Cancel

A square means times itself: sin² x = sin x × sin x.

We write every one out.

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 over sin x.

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, sin 30° × cos 30° over sin² 30° is about 1.7321.

And cot 30° is about 1.7321.

The same!

So it is right.

Let's look back.

First: cancel.

Then: name it.

Last: check.