Simplify 1 - cos^2 x

Step by step

The question

Question: simplify 1 − cos² x.

Simplify means: write it as simply as we can.

1 Use sin² + cos² = 1

The most important identity: sin² x + cos² x = 1.

It comes from the unit circle.

Moved around, it says 1 − cos² x = sin² x.

Careful!

The square stays: 1 − cos² x is sin² x, with the square.

So we put sin² x in place of (1 − cos² x).

So it simplifies to sin² x.

2 Check

Let's check with a number: x = 30°.

On the calculator, 1 − cos² 30° is about 0.2500.

And sin² 30° is about 0.2500.

The same!

So it is right.

Let's look back.

First: use sin² + cos² = 1.

Last: check.