The distance between two points (a cos α, 0) and (0, a sin α) is ___________.

Correct option is B

Given:

We need to find the distance between the two points:

​$$P (a \cos \alpha, 0) \quad \text{and} \quad Q (0, a \sin \alpha)$$​​

Formula Used:

The distance formula between two points $$(x_1, y_1)$$​ and $$(x_2, y_2)$$​is:

​$$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$​​

Solution:

D = $$\sqrt{(0 - a \cos \alpha)^2 + (a \sin \alpha - 0)^2}$$​​

D =$$\sqrt{(a \cos \alpha)^2 + (a \sin \alpha)^2}$$​​

D =$$\sqrt{a^2 \cos^2 \alpha + a^2 \sin^2 \alpha}$$​​

D=$$\sqrt{a^2 (\cos^2 \alpha + \sin^2 \alpha)}$$​​

D = $$\sqrt{a^2 \times 1} = \sqrt{a^2} =| a|$$

Option (b) is right.