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)

Answer 1

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 .