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8. Introduction to Trigonometry
easy
सत्य या असत्य लिखिए और अपने उत्तर का औचित्य दीजिए :
$\sqrt{\left(1-\cos ^{2} \theta\right) \sec ^{2} \theta}=\tan \theta$
Option A
Option B
Option C
Option D
Solution
True.
$\sqrt{\left(1-\cos ^{2} \theta\right) \sec ^{2} \theta}=\sqrt{\sin ^{2} \theta \cdot \sec ^{2} \theta}$ $\left[\because \sin ^{2} \theta+\cos ^{2} \theta=1\right]$
$=\sqrt{\sin ^{2} \theta \cdot \frac{1}{\cos ^{2} \theta}}$ $\left[\because \sec \theta=\frac{1}{\cos \theta}, \tan \theta=\frac{\sin \theta}{\cos \theta}\right]$
$=\sqrt{\tan ^{2} \theta}$
$=\tan \theta$
Standard 10
Mathematics
