Simplify sin x sec x

Step by step

The question

Question: simplify sin x × sec x.

Simplify means: write it as simply as we can.

1 Write in sin and cos

Everything is easier in sin and cos.

sec is 1 over cos.

We put them in.

Tops go on top, bottoms at the bottom.

2 Name it

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

So it simplifies to tan x.

3 Check

Let's check with a number: x = 30°.

On the calculator, sin 30° × sec 30° is about 0.5774.

And tan 30° is about 0.5774.

The same!

So it is right.

Let's look back.

First: write in sin and cos.

Then: name it.

Last: check.