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📰 Solution: Let $t = \sin x + \csc x$. Note $\tan x + \cot x = \frac{\sin x}{\cos x} + \frac{\cos x}{\sin x} = \frac{1}{\sin x \cos x}$. Let $y = \sin x \cos x = \frac{1}{2}\sin 2x$, so $\tan x + \cot x = \frac{2}{\sin 2x}$. The expression becomes $\left(\frac{2}{\sin 2x}\right)^2 + (\sin x + \csc x)^2$. Let $z = \sin x + \csc x \geq 2$ by AM-GM. Substitute $u = \sin 2x$, then minimize $\frac{4}{u^2} + \left(\frac{1}{\sin x} + \sin x\right)^2$. After calculus or substitution, the minimum occurs at $x = \frac{\pi}{4}$, yielding $(1 + 1)^2 + (\sqrt{2} + \frac{1}{\sqrt{2}})^2 = 4 + \left(\frac{3}{\sqrt{2}}\right)^2 = 4 + \frac{9}{2} = \frac{17}{2}$. However, correct simplification shows the minimum is $9$ when $x = \frac{\pi}{4}$. 📰 \boxed{9}Question: What is the smallest positive integer that is a multiple of 16 and one more than a multiple of 5? 📰 Solution: Let the integer be $ n $. We have $ n \equiv 0 \pmod{16} $ and $ n \equiv 1 \pmod{5} $. Let $ n = 16k $. Substituting into the second congruence: 📰 Charlie Kirks Net Worth At Death 5675988 📰 Yvr Airport 3698036 📰 Library For Happymood Apk Smart Start 📰 Get Rich Fast 3 Secrets Everyones Too Afraid To Share But They Work 8603408 📰 You Wont Believe The Hidden Lesson That Transformed My Entire Career At Adviseworks 93921 📰 Deepest Fear 📰 Track Id Apk 📰 D Were Imported Only After The Invention Of Metalworking 6716594 📰 Pedility Exposed Why Fitness Enthusiasts Are Obsessed And How It Transforms Your Life 7150550 📰 Big Businesses Swarm Oracle Erp Cloud Discover The Secret Power Inside 8069120 📰 Paladins Steam 8150899 📰 Charlie Kirks Wealth Shocked Fans Secrets Behind His Massive Net Worth Revealed Now 2074293 📰 Lost Your Lights Blackout Bingo Is The Secret Game Turning Minutes Into Millions 2707563 📰 Loteria Tradicional 1233875 📰 Why Black Ops 6 Ps4 Is Taking Over Steam The Hidden Ps4 Multiplayer Craze You Need 1041722