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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} 📰 Tom Cruise And Ana De Armas 2450738 📰 Below Deck Streaming 📰 This Secret Boxlayout Layout Is Taking Designers By Stormsee How 7440858 📰 The Ultimate Kingdom Hearts Iii Climax Heres Why Every Player Should Re Watch It Now 4131532 📰 Corpse Party Walkthrough 📰 Mybenefitsresources Bank Of America 📰 Palladium Price 📰 Report Reveals 70S Black Tv Shows And It Shocks Everyone 📰 Fideline Secrets Exposed You Wont Believe What This Habit Does To Your Success 7080961 📰 Winxp Sp2 Download 📰 10 Metroidvania Games That Will Blow Your Mindno Spoilers Yet 4108388 📰 You Wont Believe What This Usaid Project Is Changing Across The Nation 3515383 📰 New Runescape 📰 Bank Of America Forney 📰 Online Games Mahjong Solitaire 2208853