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📰 Solution: Expand $ (\tan x + \cot x)^2 = \tan^2 x + 2 \tan x \cot x + \cot^2 x $. Simplify using $ \tan x \cot x = 1 $: $ \tan^2 x + 2 + \cot^2 x $. Use identity $ \tan^2 x + \cot^2 x = (\tan x - \cot x)^2 + 2 $, so expression becomes $ (\tan x - \cot x)^2 + 4 $. The minimum occurs when $ \tan x = \cot x $, i.e., $ x = \frac{\pi}{4} + k\frac{\pi}{2} $, giving $ 0 + 4 = 4 $. \boxed{4} 📰 Question: Compute $ (\cos \theta + i \sin \theta)^5 $ using De Moivre’s theorem. 📰 Solution: By De Moivre’s theorem, $ (\cos \theta + i \sin \theta)^n = \cos(n\theta) + i \sin(n\theta) $. Applying $ n = 5 $, the result is $ \cos(5\theta) + i \sin(5\theta) $. \boxed{\cos(5\theta) + i \sin(5\theta)} 📰 Master Granny Square Patterns Like A Pro Step By Step Guide Inside 1042353 📰 Traductor Online 2881623 📰 Black Titiies Revealed The Scandalous Rituals That Could Change Everything 5235355 📰 Verizon Fios Track Order 4962722 📰 5Rcorrect The Key In Seconds The Proven Way To Find Your Windows 10 Product Key 9992802 📰 Inside The Trump Donor Network Billionaires Secrets Behind His Business Empire Unveiled 8417083 📰 Gamefaqs Final Fantasy Tactics 1584929 📰 Oo7 Nightfire Cheats 5862853 📰 Digestions Hidden Clock The Bizarre Delay That Turned Scientists Silent 4475254 📰 National Provider Identifier Number Application Secrets You Need To Know Now 5944698 📰 Sai Advanced Power Solutions 9328109 📰 What Are The Core Principles Behind Effective Investment Strategy For Beginners 264585 📰 From Garage Startup To Tech Gianthow Larry Ellison Redefined Leadership At Oracle 5350825 📰 Interview With A Vampire Season 2 2573894 📰 3 Unlock The Power Of 90 7 Key Factors You Need To Know Now 2945558