Option A: $\sqrt{a^2 + b^2}$
Using the distance formula: $d = \sqrt{(a\cos\theta + b\sin\theta - 0)^2 + (0 - (a\sin\theta - b\cos\theta))^2}$
$= \sqrt{a^2\cos^2\theta + 2ab\cos\theta\sin\theta + b^2\sin^2\theta + a^2\sin^2\theta - 2ab\sin\theta\cos\theta + b^2\cos^2\theta}$
$= \sqrt{a^2(\cos^2\theta + \sin^2\theta) + b^2(\sin^2\theta + \cos^2\theta)} = \sqrt{a^2 + b^2}$
Source: Chapter 7, Section 7.2 (Distance Formula)
Apply the distance formula with $(x_1, y_1) = (a\cos\theta + b\sin\theta,\ 0)$ and $(x_2, y_2) = (0,\ a\sin\theta - b\cos\theta)$. After expanding and collecting terms, the cross-terms ($2ab\sin\theta\cos\theta$) cancel, and using $\sin^2\theta + \cos^2\theta = 1$ simplifies everything neatly to $\sqrt{a^2+b^2}$. The result is independent of $\theta$ — a key observation examiners expect you to recognise.