Question

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

पर्याय

• a

• 2a

• 3a

•  None of these

Answer 1

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

In general, the distance between A(x₁ , y₁ )  and B( x₂ ,y₂ ) 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