Question

distance between two points (2,cot @)and (1,0)

Answer 1

a(2,cot ø) b(1,0) ( I have make cot à into cot ø for my ease)
using distance formula
$\sqrt{(2 - 1 ^{2}) + ( \cot\: o)^{2} }$
so
$\sqrt{1{}^{2} + cot^{2} \: o }$
we that 1+cot²ø=cosec²
$\sqrt{ {cosec}^{2} o}$
distance=cosec² ø
I hope you would like my answer and would be brainiest one ☺️

Answer 2

Answer:

The distance between the points $(1,0) and (2, \cot \theta)$ is $\ {cosec} \theta} .$

Step-by-step explanation:

Given: Two points

To find: Distance between the points

Solution:

The distance between $\left(x_{1}, y_{1}\right) and \left(x_{2}, y_{2}\right) is \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} .$

Therefore, the distance between the points $(1,0) and (2, \cot \theta)$

$&=\sqrt{(2-1)^{2}+(\cot \theta-0)^{2}}$

$&=\sqrt{(1)^{2}+(\cot \theta)^{2}}$

$&=\sqrt{1+(\cot \theta)^{2}}$

$=\sqrt{(Cosec} \theta)^{2}}$

$&=\ Cosec\theta$

Hence, the distance between the points $(1,0) and (2, \cot \theta)$ is $\ {cosec} \theta} .$