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Home » Therefore, the greatest common divisor is \(\boxed16\). - GetMeFoodie

Therefore, the greatest common divisor is \(\boxed16\). - GetMeFoodie

📅 May 1, 2026 👤 scraface

May 01, 2026

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\min (\sec x + \csc x)^2 = 8
Question: A science policy analyst is modeling the efficiency of a new...
Find the minimum value of this expression for $ x \in (0, \frac{\pi}{2...
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

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