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Home » Denominator: $6 \cdot 2 \cdot 24 \cdot 1 = 288$ - High Altitude Science

Denominator: $6 \cdot 2 \cdot 24 \cdot 1 = 288$ - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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🔥 Popular Posts

Using the Pythagorean identity $ \sin^2 x + \cos^2 x = 1 $, this becom...
f(x) = 1 + \frac{1}{\sin^2 x} + \frac{1}{\cos^2 x}
Let $ a = \sin^2 x $, $ b = \cos^2 x $, so $ a + b = 1 $, and $ a, b >...
f(x) = 1 + \frac{1}{a} + \frac{1}{b}
We now minimize $ \frac{1}{a} + \frac{1}{b} $ under the constraint $ a...
\frac{1}{a} + \frac{1}{b} \geq \frac{4}{a + b} = 4
Equality occurs when $ a = b = \frac{1}{2} $, i.e., when $ \sin^2 x =...
Substituting back:
f\left(\frac{\pi}{4}\right) = 1 + \frac{1}{\frac{1}{2}} + \frac{1}{\fr...
Thus, the minimum value of $ f(x) $ is:

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