Write 'True' or 'False' and justify your answer.
$\sqrt{(1-\cos^2 \theta) \sec^2 \theta} = \tan \theta$

(A) True.
Given expression: $\sqrt{(1-\cos^2 \theta) \sec^2 \theta}$
Using the identity $\sin^2 \theta + \cos^2 \theta = 1$,we have $1 - \cos^2 \theta = \sin^2 \theta$.
Substituting this into the expression: $\sqrt{\sin^2 \theta \cdot \sec^2 \theta}$
Since $\sec \theta = \frac{1}{\cos \theta}$,we can write: $\sqrt{\sin^2 \theta \cdot \frac{1}{\cos^2 \theta}} = \sqrt{\frac{\sin^2 \theta}{\cos^2 \theta}}$
Using the identity $\tan \theta = \frac{\sin \theta}{\cos \theta}$,we get: $\sqrt{\tan^2 \theta} = \tan \theta$.
Thus,the statement is true.