$\"\"$

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Let the rectangular coordinates of $\"\"$ be $\"\"$ and $\"\"$ be $\"\"$ .

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Distance between two points $\"\"$ and $\"\"$ in the cartesian plane is :

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$\"\"$ .

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The points $\"\"$ and $\"\"$ in the partesian coordinates are $\"\"$ and

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$\"\"$ .

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Where $\"\"$ and $\"\"$ .

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Substiute the expressions $\"\"$ and $\"\"$ in terms of the polar coordinates.

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$\"\"$

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From the trigonometric identities :

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

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By substituting the above identities the formula obtained is :

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$\"\"$

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$\"\"$

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The formula for the distance between the points with polar coordinates $\"\"$ and $\"\"$ is

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$\"\"$ .