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What is the difference between a trigonometric equation that is an identity and a trigonometric equation that is not an identity? Provide an example to clarify.

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An identity is an equality relationship between two mathematical expressions. For example, in basic algebra students are expected to master various algebraic factoring identities such as
a^2 - b^2 = (a - b)(a + b)

In trigonometry, trigonometric identities are equations involving trigonometric ...

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