Question

The distance between the points (cos θ, 0) and (sin θ − cos θ) is

पर्याय

• \[\sqrt{3}\]

   

• \[\sqrt{2}\]

   

• 2

• 1

Answer 1

We have to find the distance between ` A (cos theta , sin theta ) and B ( sin theta , - cos theta ) `. 

In general, the distance between A`(x_1 , y_1) `  and B `(x_2 , y_2)`  is given by,

`AB = sqrt ((x_2 - x_1 )^2 + ( y_2-y_1)^2)`

So,

`AB = sqrt(( sin theta - cos theta )^2 + ( - cos theta - sin theta )^2)`

      ` = sqrt( 2 ( sin ^2 theta + cos^2 theta ) `

But according to the trigonometric identity,

`sin^2 theta + cos^2 theta = 1`

Therefore,

AB = `sqrt (2) `