$\"\"$

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The trigonometric identity is $\"\"$ .

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Consider the left side of the identity : $\"\"$ .

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Reciprocal identity : $\"\"$ .

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$\"\"$

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Apply half-angle formula : $\"\"$ .

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$\"\"$

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Reciprocal identity : $\"\"$ .

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$\"\"$

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= Right hand side identity.

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$\"\"$

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$\"\"$ .