Используем формулы разность синусов и разность косинусов:
sin(a) - sin(b) ≡ 2·sin( (a-b)/2 )·cos( (a+b)/2).
cos(a) - cos(b) ≡ -2·sin( (a+b)/2)·sin( (a-b)/2).
Тогда sin(5a) - sin(7a) ≡ 2·sin( (5a - 7a)/2)·cos( (5a+7a)/2) ≡
≡ 2·sin(-a)·cos(6a) ≡ -2·sin(a)·cos(6a).
cos(7a) - cos(5a) = -2sin( (7a+5a)/2)·sin( (7a - 5a)/2) ≡
≡ - 2sin(6a)·sin(a).
левая часть ≡ 
