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📰 Question: Find the maximum value of $ (\sin x + 2\cos x)^2 + \sin^2 x $. 📰 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} 📰 This Lion And The Kings Ultimate Showdown Characters You Never Knew Mattered 36443 📰 Wells Fargo Bank Appointments 2377264 📰 Never Known How To Open Settings In Windows 11 Heres Your Shocking Fix 6787089 📰 Java Development Kit For Mac 6666736 📰 You Wont Believe What Happens When You Forget Your Planner Center Password 6489384 📰 The Handmaids Tale Season 4 9640401 📰 South Straub Park 2506542 📰 Copy Paste Not Working 4839939 📰 403 Roblox Error 1416580 📰 Shocked By This Super Mario Tri Loop Masterpiecesuper Mario Bros 3 Uncovered 9341517 📰 From First Light To Clean Teethsunrise Dental Brooklyn 68 Is The Hit Youve Been Searching For 1543474 📰 Enron Stock 3446083 📰 Savannah Bananas Players 2176796 📰 The Truth About Fidelity Wise Origin Bitcoin Fund Thousands Are Ratings Blinding You 3264098 📰 Best Games On Windows 1603752