Word Count : 271

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Consider the expression ( f(x) = a^2 \sec^2 x + b^2 \csc^2 x ), where ( a > 0 ) and ( b > 0 ). We can rewrite it using (\sec^2 x = 1 + \tan^2 x) and (\csc^2 x = 1 + \cot^2 x): [ f(x) = a^2 (1 + \tan^2 x) + b^2 (1 + \cot^2 x) = a^2 + a^2 \tan^2 x + _______ __________ ________ _____ _____ ______ _________ _____ ______ ___ _____ _________.
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