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Home » Scaling by 2 multiplies the entire transformation matrix by 2: - Abu Waleed Tea

Scaling by 2 multiplies the entire transformation matrix by 2: - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \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 becomes:

📌 + y + \frac{1}{y}

📌 We minimize $y + \frac{1}{y}$ for $y > 0$. By AM-GM inequality:

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