What is (\sec \theta - \tan \theta) - \sqrt{\frac{1 - \sin \theta}{1 + \sin \theta}} equal to?

Explanation

Rationalizing the term inside the square root: \sqrt{\frac{1 - \sin \theta}{1 + \sin \theta} \cdot \frac{1 - \sin \theta}{1 - \sin \theta}} = \sqrt{\frac{(1 - \sin \theta)^2}{\cos^2 \theta}} = \frac{1 - \sin \theta}{\cos \theta} = \sec \theta - \tan \theta. Subtracting this from the first term yields 0.

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