Используя тождество sin^2a+cos^2a, упростите выражения: 1) sin^4a+2sin^2a cos^2a+cos^4a 2) (sina+cosa)^2+(sina-cosa)^2 3) cos^2a-cos^4a+sin^4a

[latex]1) sin^4a + 2sin^2a*cos^2a + cos^4a = (sin^2a+cos^2a)^2 = 1[/latex] [latex]2) (sina + cosa)^2 + (sina - cosa)^2 \\ (sina + cosa)^2 = sin^2a + 2sina*cosa + cos^2a \\ (sina - cosa)^2 = sin^2a - 2sina*cosa + cos^2a \\ sin^2a + 2sina*cosa + cos^2a + sin^2a - 2sina*cosa + cos^2a = \\ 2(sin^2a + cos^2a) = 2[/latex] [latex]3)cos^2a - cos^4a + sin^4 a \\ cos^2a*(1 - cos^2a) + sin^4a \\ cos^2a*sin^2a + sin^4a \\ sin^2(cos^2 + sin^2a) = sin^2a[/latex]