Rewrite the expression (tan A)(cot A) in terms of a single trigonometric ratio.

looks like "homework dumping" to me

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To rewrite the expression (tan A)(cot A) in terms of a single trigonometric ratio, we can use the identity:

tan A = 1 / cot A

Thus, we can substitute this identity into our expression:

(tan A)(cot A) = (1 / cot A)(cot A)

Now, the cot A terms cancel out:

= 1

Therefore, the expression (tan A)(cot A) simplifies to 1.