The value of \((\sec A + \tan A)(1 - \sin A)\) is:
Answer: B
Let's convert everything to sines and cosines.
\((\frac{1}{\cos A} + \frac{\sin A}{\cos A})(1 - \sin A)\)
= \(\frac{1+\sin A}{\cos A}(1 - \sin A)\)
= \(\frac{(1+\sin A)(1-\sin A)}{\cos A}\)
= \(\frac{1 - \sin^2 A}{\cos A}\)
Using the identity \(1 - \sin^2 A = \cos^2 A\), the expression becomes:
\(\frac{\cos^2 A}{\cos A} = \cos A\).