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**Verifying Trigonometric Identities**

Digital Lesson Verifying Trigonometric Identities

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**Guidelines for Verifying Identities**

1. Start with the most complicated side of the equation. 2. Factor an expression, add fractions, square a binomial, or create s monomial denominator, if possible. 3. Use the fundamental identities, whenever possible. 4. Convert all terms to sines and cosines. 5. Always try something. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Guidelines for Verifying Identities

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**Example: Verify Identity**

Verify the identity Start with the more complicated side. Pythagorean Identity Simplify. Reciprocal Identity Quotient Identity Simplify. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Example: Verify Identity

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**Graphing Utility: Verify Identity**

Verify the identity Identical Values Table: Identical Graphs –2 2 –0.5 1.5 –2 2 –0.5 1.5 Graph: Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Graphing Utility: Verify Identity

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**Example: Verify Identity**

Verify the identity Pythagorean Identity Reciprocal Identity Rule of Exponents Quotient Identity Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Example: Verify Identity

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**Sum and Difference Formulas**

Signs are the same Example: Verify the identity Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Sum and Difference Formulas

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**Sum and Difference Formulas (continued)**

Signs are opposite Signs are the same Signs are the same Opposite signs Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Sum and Difference Formulas (continued)

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**Double-Angle Formulas**

Example: Verify the identity Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Double-Angle Formulas

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**Double-Angle Formulas (continued)**

Example: Verify the identity Sum Formula Double-Angle Formula Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Double-Angle Formulas (continued)

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**Half-Angle Formulas: Example:**

Use the half-angle formula to find the exact value of sin 22.5°. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Half-Angle Formulas

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