Given that cos z = L, where z is an acute angle, we need to find an expression for cot z - csc z sec z + tan z.
We can start by using the identity cos^2 z + sin^2 z = 1 to obtain sin z = sqrt(1 - L^2).
Next, we can substitute sin z and cos z in the expression to get:
cot z - csc z sec z + tan z
= cos z / sin z - 1 / (sin z * cos z) + sin z / cos z
= (cos^2 z - 1 + sin^2 z) / (sin z * cos z)
= (L^2 - 1 + 1 - L^2) / sqrt(1 - L^2)
= -sqrt(1 - L^2)
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Therefore, the expression for cot z - csc z sec z + tan z is -sqrt(1 - L^2)