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Verifying Trigonometric Identities

Verifying Trigonometric Identities. In verifying identities, we are trying to demonstrate that the left side of the identity is equivalent to the right side of the identity .

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Verifying Trigonometric Identities

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  1. Verifying Trigonometric Identities • In verifying identities, we are trying to demonstrate that the left side of the identity is equivalent to the right side of the identity. • In verifying identities, do not think of the process as solving an equation. For example, don’t add the same expression to both sides. • We do not know that the left side is equal to the right side in an identity. That is what we are trying to prove.

  2. Process to Verify an Identity • Start with one side, usually the more complicated side. • Use identities to simplify and change form. • Use algebraic manipulation: multiply up and down by the same expression, factor expressions, etc. • Try writing all trigonometric expressions in terms of sine and cosine. • Keep working until you get the expression on the other side of the identity.

  3. Example 1: • Verify the identity: • Start with the left side, and try to use valid operations to get the right side.

  4. Example 2: • Verify the identity: • Start with the left side, and try to use valid operations to get the right side.

  5. Example 3: • Verify the identity:

  6. Example 4: • Verify the identity:

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