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Home » Taking reciprocals (since all terms are positive): - Anadea

Taking reciprocals (since all terms are positive): - Anadea

📅 May 15, 2026 👤 scraface

May 15, 2026

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Solution: Expand both squares:
\cos^2 x + \sin^2 x + 4 + \sec^2 x + \csc^2 x = 1 + 4 + rac{1}{\cos^2...
So total expression is:
+ \sec^2 x + \csc^2 x = 5 + rac{1}{\cos^2 x} + rac{1}{\sin^2 x}
Write as:
+ rac{\sin^2 x + \cos^2 x}{\sin^2 x \cos^2 x} = 5 + rac{1}{\sin^2 x...
But \(\sin^2 x \cos^2 x = rac{1}{4} \sin^2 2x\), so:
= 5 + rac{4}{\sin^2 2x}
Minimum occurs when \(\sin^2 2x\) is maximized, i.e., \(\sin^2 2x = 1\...
Then value is \(5 + 4 = 9\)

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