упростите выражение [tex](cosa + 2sina)^2-2sin2a-1[/tex]. Created by nikitaaz. algebra-ru

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Madlen666

(cosa + 2sina)^2-2sin2a-1=cos^2a+4sina*cosa+4sin^2a-4sina*cosa-cos^2a-sin^2a=3sin^2a

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Voxman

$(cosa + 2sina)^2-2sin2a-1 =\\\\ cos^2a + 4cosasina + 4sin^2a - 2sin2a - 1 =\\\\ cos^2a + 4cosasina + sin^2a + 3sin^2a - 2sin2a - 1 =\\\\ \underline{cos^2a + sin^2a} + 2sin2a + 3sin^2a - 2sin2a - 1 =\\\\ 1 + \underline{2sin2a} - \underline{2sin2a} + 3sin^2a - 1 =\\\\1 + 3sin^2a - 1 = 3sin^2a\\\\\\ sin^2a + cos^2a = 1,\\\\2sinacosa = sin2a$

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