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Home » 9c^2 \left(1 - racz^2x^2 + y^2 + z^2 - Veritas Home Health

9c^2 \left(1 - racz^2x^2 + y^2 + z^2 - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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+ 2 + 2 + \cot^2 x + \tan^2 x = 5 + \cot^2 x + \tan^2 x.
Let $t = \tan^2 x$, so $\cot^2 x = \frac{1}{t}$. The expression become...
+ t + \frac{1}{t}.
By AM-GM, $t + \frac{1}{t} \geq 2$, with equality when $t = 1$ (i.e.,...
Actually, $\sin x + \csc x = \sin x + \frac{1}{\sin x} \geq 2$, and si...
But the sum is minimized at $8$ (when $x = \frac{\pi}{4}$), but maximu...
At $x = \frac{\pi}{4}$, $\sin x = \cos x = \frac{\sqrt{2}}{2}$, $\csc...
\left(\frac{\sqrt{2}}{2} + \sqrt{2}\right)^2 + \left(\frac{\sqrt{2}}{2...
Thus, the minimum is $9$. But the question asks for the maximum, which...
\boxed{9}

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