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.

#### Example 2

Simplify .

#### Example 3

Verify .

### Review

Simplify the following expressions.

Verify the following identities.

### Answers for Review Problems

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