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Home » 5) **Curious How to Make Purple? Here’s the HIDDEN Trick You Didn’t Know! - Dachbleche24

5) **Curious How to Make Purple? Here’s the HIDDEN Trick You Didn’t Know! - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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This can be expanded as:
Notice that \(\sec \theta = \frac{1}{\cos \theta}\) and \(\csc \theta...
\cos^2 \theta + 2 + \sec^2 \theta + \sin^2 \theta + 2 + \csc^2 \theta
Using the Pythagorean identity \(\cos^2 \theta + \sin^2 \theta = 1\),...
+ 2 + \sec^2 \theta + 2 + \csc^2 \theta = 5 + \sec^2 \theta + \csc^2 \...
Recall the identities \(\sec^2 \theta = 1 + \tan^2 \theta\) and \(\csc...
+ \sec^2 \theta + \csc^2 \theta = 7 + \tan^2 \theta + \cot^2 \theta
Using the AM-GM inequality, \(\tan^2 \theta + \cot^2 \theta \geq 2\),...
+ \tan^2 \theta + \cot^2 \theta \geq 7 + 2 = 9
The minimum value is achieved when \(\tan^2 \theta = \cot^2 \theta = 1...

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