Answer
8 $|\cos\theta|$
Work Step by Step
Given expression-
$ \sqrt {64 - 4x^{2}}$
Substituting $4\sin\theta$ for $x$ as given, the expression becomes-
$ \sqrt {64 - 4(4\sin\theta)^{2}}$
= $ \sqrt {64 - 4(16\sin^{2}\theta)}$
= $ \sqrt {64 - 64\sin^{2}\theta}$
= $ \sqrt {64(1 - \sin^{2}\theta)}$
= $ \sqrt {64\cos^{2}\theta}$
{ Writing $(1 - \sin^{2}\theta)$ as $ \cos^{2}\theta$ using first Pythagorean identity}
= 8 $|\cos\theta|$
