Question

Найти sin3a-cos3a, если sina-cosa=m

Answer 1

81(sin^3(a) + cos^3(a)) = 81(sin(a) + cos(a))(sin^2(a) - sin(a)cos(a) + cos^2(a)) = (81/3)(1 - 0.5sin(2a)) = (*)

sin^2(a) + cos^2(a) + sin(2a) = 1 + sin(2a) = 1/9 => sin(2a) = 1/9 - 1 = -8/9

(*) = (81/3)(1 + 8/18) = (81/3)(26/18) = 39