Pre-Calculus 12 Notes

By: Gen L.

Lesson 4: Double Angle Identities

Sine Double Angle

Let's derive it:

Sine Identities

Cosine Double Angle

Let's derive it:

First Cosine Identity

Cosine Double Angles, part I

Starting from 13: , we can get the other two cosine double angle identities.

Cosine Double Angles, part II

Starting from 13: , we can get the other two cosine double angle identities.

Cosine Double Angles

Here are our 3 identities for

13. for both sine and cosine.
14. for only sine.
15. for only cosine.

Tangent Double Angle

Last is for . Let's derive it:

Proving w/ Double Angle

Besides simplifying double angles to single angles, you will use them to prove identities. Like this one:

More Proofs

How about a challenge?

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