Question

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

(a) a

(b) 2a

(c) 3a

(d) None of these

Answer 1

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

In general, the distance between A and B is given by,

So,

$$\begin{gathered} AB=\sqrt{{\left(0-a\cos 25°\right)}^2+{\left(a\cos 65°-0\right)}^2} \\ =\sqrt{{\left(a\cos 25°\right)}^2+{\left(a\cos 65°\right)}^2} \end{gathered}$$

$\cos 25°=\sin 65°\mathrm{and}\cos 65°=\sin 25°$

But according to the trigonometric identity,

Therefore,

So, the answer is (a)