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Question
Find the distance between the following point :
(Sin θ - cosec θ , cos θ - cot θ) and (cos θ - cosec θ , -sin θ - cot θ)
Solution
A (Sin θ - cosec θ , cos θ - cot θ)
B (cos θ - cosec θ , -sin θ - cot θ)
AB = `sqrt (("cos" theta - "cosec" theta - "sin" theta + "cosec" theta)^2 + (- "sin" theta - "cot" theta - "cos" theta + "cot" theta)^2)`
`= sqrt (("cos" theta - "sin" theta)^2 + (- "sin" theta - "cos" theta)^2)`
`= sqrt ("cos"^2 theta + "sin"^2 theta - 2 "cos" theta "sin" theta + "sin"^2 theta + "cos"^2 theta + 2 "sin" theta "cos" theta)`
`= sqrt 2` units .
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