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📰 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)} 📰 Question: Find the range of $ f(x) = \frac{2\sin x + 1}{\sin x - 3} $ for $ x $ where the denominator is nonzero. 📰 Solution: Let $ y = \frac{2\sin x + 1}{\sin x - 3} $. Solve for $ \sin x $: $ y(\sin x - 3) = 2\sin x + 1 \Rightarrow y\sin x - 3y = 2\sin x + 1 \Rightarrow \sin x(y - 2) = 3y + 1 $. Thus, $ \sin x = \frac{3y + 1}{y - 2} $. Since $ |\sin x| \leq 1 $, solve $ \left| \frac{3y + 1}{y - 2} \right| \leq 1 $. This leads to $ -1 \leq \frac{3y + 1}{y - 2} \leq 1 $. Sol 📰 32000 7022325 📰 How To Check Your Npi Number Fastno Tech Skills Required 3793626 📰 Hchd Login 7949049 📰 Ai Revolution Unleashed The Fin Readiest Stocks To Buy In 2025 827418 📰 No Tomatoes No Problem Crazy Effective Sauce Substitutes You Need To Know 9139742 📰 Gangster Beasts Unleashed Behind The Chaos Of Living Nightmares 70161 📰 Epic Games Fortnite Og 1363267 📰 Master Microsoft Excel With This Fastest Keyboard Trick To Delete Rows 7405374 📰 The Reasons Simbramento Haunts Generationsyou Need To Know Before Its Too Late 6812128 📰 Columbus Ohio Water Bill 3402820 📰 You Wont Believe What The Department Of Health And Human Services Doesaction You Must See 6233537 📰 Caa Agency 7709242 📰 A Tear Stunned Gaze A Silent Hug Only The Faintest Heart Can Hear 9058664 📰 Daily Growth Factor 1 015 115 6845624 📰 Youll Never Guess Your True Agethis Chronological Age Calculator Rewrites Everything 8409662