Вычислите sin^6a+cos^6a
Если sina+cosa=0.4

Смотреть во вложении

sin^6 a + cos^6 a = (sin^2 a)^3 + (cos^2 a)^3 = = (sin^2 a + cos^2 a)(sin^4 a - sin^2 a*cos^2 a + cos^4 a) == 1*(sin^4 a - sin^2 a*cos^2 a + cos^4 a) = = sin^4 a + 2sin^2 a*cos^2 a + cos^4 a - 3sin^2 a*cos^2 a == (sin^2 a + cos^2 a)^2 - 3sin^2 a*cos^2 a = 1 - 3sin^2 a*cos^2 aТак как sin a + cos a = 0,4, то (sin a + cos a)^2 = sin^2 a + 2sin a*cos a + cos^2 a = 0,4^2 = 0,161 + 2sin a*cos a = 0,16sin a*cos a = (0,16 - 1)/2 = -0,84/2 = -0,421 - 3*sin^2 a*cos^2 a = 1 - 3*(-0,42)^2 = 1 - 3*0,1764 = 0,4708