MCQ

The distance between the points (*a* cos 25°, 0) and (0, *a* cos 65°) is

#### Options

a

2a

3a

None of these

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#### Solution

We have to find the distance between A(*a* cos 25°, 0) and B (0 , a cos 65° ) .

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,

\[AB = \sqrt{\left( 0 - a\cos25° \right)^2 + \left( a\cos65° - 0 \right)^2}\]

\[ = \sqrt{\left( a\cos25° \right)^2 + \left( a\cos65° \right)^2}\]

\[\cos25° = \sin65° and \cos65° = \sin25° \]

But according to the trigonometric identity,

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

Therefore,

**AB = a**

Concept: Coordinate Geometry

Is there an error in this question or solution?

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