Question:
$\sqrt{\left(1-\cos ^{2} \theta\right) \sec ^{2} \theta}=\tan \theta$
Solution:
True
$\sqrt{\left(1-\cos ^{2} \theta\right) \sec ^{2} \theta}=\sqrt{\sin ^{2} \theta \cdot \sec ^{2} \theta}$ $\left[\because \sin ^{2} \theta+\cos ^{2} \theta=1\right]$
$=\sqrt{\sin ^{2} \theta \cdot \frac{1}{\cos ^{2} \theta}}=\sqrt{\tan ^{2} \theta}=\tan \theta \quad\left[\because \sec \theta=\frac{1}{\cos \theta}, \tan \theta=\frac{\sin \theta}{\cos \theta}\right]$
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