$\"\"$

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The trigonometric identity is $\"\"$ .

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Left hand side identity $\"\"$ .

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Sum formula of sine function: $\"\"$ .

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$\"\"$

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$\"\"$

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Take out common factor $\"\"$ .

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$\"\"$

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= right hand side identity.

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Thus, $\"\"$ .

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$\"\"$

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The identity $\"\"$ is verified.