Answer:
sec²(x)
Explanation:
As required:
... = (sin²(x)/cos²(x))(1 +(cos²(x)/sin²(x))
... = (sin²(x)·(sin²(x)+cos²(x)) / (cos²(x)·sin²(x))
... = 1/cos²(x) = sec²(x)
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Alternatively, multiply out the given expression, then use trig identities.
... = tan²(x) + (tan(x)·cot(x))² = tan²(x) +1 = sec²(x)
