Question

Найти значение выражения 81(sin^3 a + cos^3 a), если sin a +cos a= 1/3. Срочно

Answer 1

sin a + cos a = 1/3
(sin a + cos a) ^2 = 1/9
sin ^2 a + 2 sin a* cos a + cos ^2 a = 1/9
1+2sin a* cos a= 1/9
sin a * cos a = -4/9

sin^3 a + cos^3 a = (sin a+cos a)(sin^2 a -sin a * cos a + cos^2 a)= 1/3*(1+4/9)=13/27

81(sin^3 a + cos^3 a)=39