Question

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

Answer 1

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 a
Так 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 = 0,16
1 + 2sin a*cos a = 0,16
sin a*cos a = (0,16 - 1)/2 = -0,84/2 = -0,42
1 - 3*sin^2 a*cos^2 a = 1 - 3*(-0,42)^2 = 1 - 3*0,1764 = 0,4708

Answer 2

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