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Home » Why Everyone’s Talking About the Lizzie Borden Rhyme (You Won’t Believe What It Reveals!) - Network4

Why Everyone’s Talking About the Lizzie Borden Rhyme (You Won’t Believe What It Reveals!) - Network4

📅 May 20, 2026 👤 scraface

May 20, 2026

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Question: Find the minimum value of $ (\cos x + \sec x)^2 + (\sin x +...
Expand both terms:
= \cos^2 x + 2\cos x \sec x + \sec^2 x + \sin^2 x + 2\sin x \csc x + \...
Since $ \cos x \sec x = 1 $, $ \sin x \csc x = 1 $, and $ \cos^2 x + \...
= 1 + 2(1) + \sec^2 x + 2(1) + \csc^2 x = 1 + 2 + 2 + \sec^2 x + \csc^...
Now write in terms of sine and cosine:
\sec^2 x = \frac{1}{\cos^2 x}, \quad \csc^2 x = \frac{1}{\sin^2 x}
\Rightarrow \text{Expression} = 5 + \frac{1}{\cos^2 x} + \frac{1}{\sin...
Use identity:
\frac{1}{\cos^2 x} + \frac{1}{\sin^2 x} = \frac{\sin^2 x + \cos^2 x}{\...

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