$\"\"$

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If $\"\"$ prove that $\"\"$ .

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Definition of inverse trigonometric function : $\"\"$ .

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$\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$ .

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Chain rule of derivative: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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From Pythagorean theorem,

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The square of the hypotenuse is equal to sum the squares of the other two sides.

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$\"\"$

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$\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ where $\"\"$ .

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$\"\"$

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$\"\"$ where $\"\"$ .