Double Angle Identities

Examples, solutions, videos, worksheets, games and activities to help PreCalculus students learn about the double angle identities.

The following diagram gives the Double-Angle Identities. Scroll down the page for more examples and solutions.

 

What are the Double-Angle Identities or Double-Angle Formulas?
sin(2x) = 2sin(x)cos(x)
cos(2x) = cos²(x) - sin²(x) = 1 - 2sin²(x) = 2cos²(x) - 1

How to use the Double-Angle Identities or Double-Angle Formulas?
Double-Angle Formulas
A few examples that use double-angle formulas from trigonometry.

Using Double Angle Identities to Solve Equations

How to proof the Double-Angle Identities or Double-Angle Formulas?
Double Angle Formulas :
The double angles sin(2x) and cos(2x) can be rewritten as sin(x + x) and cos(x + x).
Applying the cosine and sine addition formulas, we find that sin(2x) = 2sin(x)cos(x).
Also, cos(2x) = cos²(x) - sin²(x)
How to use the sine and cosine addition formulas to prove the double-angle formulas.

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