Question

please prove this question

Answer 1

hope this helps you☺️

Answer 2

Given,

$\sqrt{\frac{1- \sin \theta}{1 + \sin \theta}} \\ \\ = \sqrt{\frac{(1- \sin \theta)(1-\sin\theta)}{(1 + \sin \theta)(1-\sin \theta) }} \\ \\ = \sqrt{\frac{(1- \sin \theta)^{2}}{1 - \sin^{2} \theta}} \\ \\ = \sqrt{\frac{(1- \sin \theta)^{2}}{\cos^{2}\theta}} \\ \\ = \frac{1 - \sin\theta}{\cos\theta} \\ \\ = \frac{1}{\cos\theta} - \frac{\sin\theta}{\cos\theta} \\ \\ = \sec\theta - \tan\theta \qquad \textbf{Proved.}$