sin n/5 cos 3n/10+cos n/5 sin 3n/10=

sin(π/5)cos(3π/10) + sin(3π/10)cos(π/5) = sin(π/5 + 3π/10) = sin(2π/10 + 3π/10) = sin(5π/10) = sin(π/2) = 1

sin (n/5+3n/10)=sin(2n+3n/10)=sin (5n/10)=sin(n/2)