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Question
The distance between the points (cos θ, 0) and (sin θ − cos θ) is
Options
- \[\sqrt{3}\]
- \[\sqrt{2}\]
2
1
Solution
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) `
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