Discussion

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:

\(\frac{\cos^2 A}{\cos A} = \cos A\).

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