$\"\"$

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The trigonometric identity is $\"fraction$ .

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Start with the left side,

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$\"equal$

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$\"equal$ (Apply reciprocal identity: $\"italic$ )

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$\"equal$ (Simplify)

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+

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Apply commutative property of addition: a + b = b + a.

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$\"equal$

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$\"equal$ (Apply pythagorean identity: $\"Syntax$ )

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$\"equal$ (Simplify)

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$\"equal$ (Take out common term 2)

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$\"equal$ (Cancel common term)

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$\"equal$ (Apply reciprocal identity: $\"italic$ )

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Then left side identity and right side identity is equal. $\"\"$

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The trigonometric identity is established.

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$\"\"$

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$\"\"$

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The trigonometric identity is $\"fraction$ .

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Start with the left side,

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$\"equal$

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$\"equal$ (Multiply numerator and denominator by $\"fraction$ )

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$\"equal$ (Simplify)

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$\"equal$ (Simplify)

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$\"equal$ (Simplify)

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$\"equal$ (Apply reciprocal identity: $\"fraction$ )

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$\"Syntax$ (Simplify)

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$\"Syntax$ (Apply standard division form: $\"fraction$ )

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$\"Syntax$ (Apply reciprocal identity: $\"italic$ )

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Then left side identity and right side identities are equal. $\"\"$

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Having arrived at the right side, the identity is established.

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$\"italic$

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$\"\"$