Word Count : 280

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We need to find the least value of the function: \[ f(x) = a^2 \sec^2 x + b^2 \csc^2 x \] where \( a > 0 \) and \( b > 0 \). ### Step 1: Express in Terms of \( \sin x \) and \( \cos x \) Rewriting secant and cosecant: \[ f(x) = a^2 \frac{1}{\cos^2 x} + b^2 \frac{1}{\sin^2 x} \] Define \( u = \cos^2 x ___ ______ ________ ______ _______ _________.
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