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# The Distance Between the Points (Cos θ, 0) and (Sin θ − Cos θ) is - Mathematics

MCQ

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

#### Options

• $\sqrt{3}$

• $\sqrt{2}$

• 2

• 1

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#### 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)

Is there an error in this question or solution?
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 6 Co-Ordinate Geometry
Q 1 | Page 63
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