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Home » \( n = 20 \) (since \( n \) must be positive) - Londonproperty

\( n = 20 \) (since \( n \) must be positive) - Londonproperty

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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We expand both terms:
\sin^2 x + \cos^2 x + \sec^2 x + \csc^2 x + 2(\tan x + \cot x)
Use identity $ \sin^2 x + \cos^2 x = 1 $, and:
+ (1 + \tan^2 x) + (1 + \cot^2 x) + 2(\tan x + \cot x) = 3 + \tan^2 x...
Let $ t = \tan x + \cot x $. Then:
\tan^2 x + \cot^2 x = t^2 - 2
+ (t^2 - 2) + 2t = t^2 + 2t + 1 = (t + 1)^2
Now, $ t = \tan x + \cot x \geq 2 $ by AM-GM, with equality when $ \ta...
So minimum occurs at $ t = 2 $, giving:
$$Question: A right triangular solar panel on a spacecraft has a hypot...

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