Sin^3(П+i)=(sin(П)cos(i)+cos(П)sin(i))^3=-sin^3(i)
Sin^3(-П+2i)=(sin(-П)cos(2i)+cos(-П)sin(2i))^3=sin^3(2i)
Sin^5(П+i)=(sin(П)cos(i)+cos(П)sin(i))^5=-sin^5(i)
Sin^5(-П+2i)=(sin(-П)cos(2i)+cos(-П)sin(2i))^5=sin^5(2i)

получается
(-sin^3(i))/3 -(sin^3(2i))/3 - (-sin^5(i))/5 + (sin^5(2i))/5


sin(i*x) = i*sh(x)

-sin^3(i)=-i*sh^3(1)
sin^3(2i)=i*sh^3(2)
-sin^5(i)=-i*sh^5(1)
sin^5(2i)=i*sh^5(2)

так?