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# Simplifying Trigonometric Expressions with Double-Angle Identities

## Simplify sine, cosine, and tangent of angles multiplied or divided by 2.

Estimated10 minsto complete
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Practice Simplifying Trigonometric Expressions with Double-Angle Identities
Progress
Estimated10 minsto complete
%
Simplifying Trig Expressions using Double and Half Angle Formulas

As Agent Trigonometry, you are given the following cryptic clue. How could you simplify this clue?

### Simplifying Trigonometric Expressions

We can also use the double-angle and half-angle formulas to simplify trigonometric expressions.

Let's simplify .

Use and then factor.

Now, let's find the formula for .

You will need to use the sum formula and the double-angle formula.

Finally, let's verify the identity .

Simplify the left-hand side use the half-angle formula.

### Examples

#### Example 1

Earlier, you were asked to simplify .

Use and then factor.

Simplify .

Verify .

### Review

Simplify the following expressions.

Verify the following identities.

To see the Review answers, open this PDF file and look for section 14.16.

### Notes/Highlights Having trouble? Report an issue.

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