$\"\"$

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The trigonometric identity is $\"\"$ .

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Consider right hand side of the identity : $\"\"$ .

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Apply product to sum formula: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Apply reduction formulas: $\"\"$ and $\"\"$ .

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$\"\"$

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= Left hand side.

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Therefore, $\"\"$ .

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$\"\"$

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$\"\"$ .