What is the value of \(\sec A(1 - \sin A)(\sec A + \tan A)\)?
1
Expand: sec A·(1 − sin A)·(sec A + tan A) = (1 − sin A)·(sec²A + sec A·tan A).
sec²A = 1/cos²A, sec A·tan A = sin A/cos²A. So (1 − sin A)·(1 + sin A)/cos²A = (1 − sin²A)/cos²A = cos²A/cos²A = 1.
So the expression equals 1.
Hence, 1.
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