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Simplifying Trigonometric Expressions with Double-Angle Identities

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

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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.

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.

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