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Find the range of the function f(x) = 3 tan^2x + 12 cot^2x + 5

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Find the range of the function f(x) = 3 tan2x + 12 cot2x + 5

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Given f(x) = 3tan2x + 12cot2x + 5

= (3tan2 x + 12cot2x) + 5

= (3tan2x + 12cot2x) + 5 ≥ 12 + 5 = 17,

since A.M ≥ G.M Thus, Rf = [17, ∞)

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