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📰 Solution: Expand $ (\sin x + 2\cos x)^2 = \sin^2 x + 4\sin x \cos x + 4\cos^2 x $. Add $ \sin^2 x $: total $ 2\sin^2 x + 4\sin x \cos x + 4\cos^2 x $. Simplify using identities: $ 2(1 - \cos^2 x) + 2\sin 2x + 4\cos^2 x = 2 + 2\cos^2 x + 2\sin 2x $. Let $ u = \cos^2 x $, $ \sin 2x = 2\sin x \cos x $. Alternatively, rewrite original expression as $ \sin^2 x + 4\sin x \cos x + 4\cos^2 x + \sin^2 x = 2\sin^2 x + 4\sin x \cos x + 4\cos^2 x $. Let $ f(x) = 2\sin^2 x + 4\sin x \cos x + 4\cos^2 x $. Use $ \sin^2 x = rac{1 - \cos 2x}{2} $, $ \cos^2 x = rac{1 + \cos 2x}{2} $, $ \sin x \cos x = rac{\sin 2x}{2} $: 📰 $ f(x) = 2\left(rac{1 - \cos 2x}{2} 📰 ight) + 4\left(rac{\sin 2x}{2} 📰 For Each Village The Number Surveyed Is 10 Of Its Population 1022664 📰 This Hidden Morimoto Lights Secret Turned His Cooking Game Around Forever 7229954 📰 Things 3 Uncovered The Hidden Reasons Experts Are Obsessed With These Simple Items 7530155 📰 Is The Stock Market Open All Day Today 9491693 📰 Cast Of The Marlow Murder Club 8982831 📰 Goluchas The Hidden Truth Behind The Laughter And The Lies 7993967 📰 Yahoo Message Board 4366223 📰 Bari Weiss 8426240 📰 Discover What Ia With Fidelity Meansand Why Everyones Obsessed 6124372 📰 Barron Trump Birthday 9103960 📰 Verizon Lays Off Thousands In November 2025Exclusive Analysis Of The Huge Cuts 6885169 📰 Costco Stock Yahoo 1097699 📰 The Mtsu Pipeline Is Changing Everythingwhat No Ones Talking About 2863276 📰 Finally Secure Encrypted Email Outlook That Keeps Your Messages Truly Private 6687358 📰 1942 Penny Value Surprising Collectors Are Rushing To Buy This Rare Coin 2964210