$\"\"$

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The trigonometric identity is $\"\"$ .

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

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$\"\"$

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$\"\"$

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

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$\"\"$

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Pythagorean identity : $\"\"$ .

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$\"\"$

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=Right hand side of the identity.

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$\"\"$

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$\"\"$ .