Explanation

This tests the Pythagorean trigonometric identity; the intended item is the standard one with x = a sec θ and y = b tan θ (the θ-powers are garbled in the transcription). The expression (a/x - b/y)(a/x + b/y) is a difference of squares: (a/x)² - (b/y)². Since a/x = sec θ and b/y = tan θ, this becomes sec²θ - tan²θ, which equals 1 by the fundamental identity. Options (c) and (d) are what you get if you expand without applying the identity. Hence option (b).