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📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📝 Recent Posts

We begin by expanding the expression:
Recall that $\cos x \sec x = 1$ and $\sin x \csc x = 1$, so the expres...
\cos^2 x + \sin^2 x + 2 + \sec^2 x + \csc^2 x + 2
Since $\cos^2 x + \sin^2 x = 1$, this simplifies to:
+ 2 + \sec^2 x + \csc^2 x + 2 = 5 + \sec^2 x + \csc^2 x
Now, write $\sec^2 x = 1 + \tan^2 x$ and $\csc^2 x = 1 + \cot^2 x$:
+ (1 + \tan^2 x) + (1 + \cot^2 x) = 7 + \tan^2 x + \cot^2 x
Let $y = \tan^2 x$, so $\cot^2 x = \frac{1}{y}$. Then the expression b...
+ y + \frac{1}{y}
We minimize $y + \frac{1}{y}$ for $y > 0$. By AM-GM inequality:

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