1st we find m+n m+n=a(sina+cosa)(sina^2+cosa^2-(sinacosa)+3sinacosa(sina+cosa) =a(sina+cosa)[(sina^2+cosa^2-(sinacosa)+3sinacosa] =a(sina+cosa)[(sina^2+cosa^2+2sinacosa] =a(sina+cosa)(sina+cosa)^2 =a(sina+cosa)^3 similerly m-n=a(cosa-sina)^3 (m+n)^2/3+(m-n)^2/3=a^2/3[(cosa+sina)^2+(cosa-sina)^2] =a^2/3[(sina^2+cosa^2+2sinacosa)+(sina^2+cosa^2-2sinacosa)] =a^2/3[(sina^2+cosa^2)+(sina^2+cosa^2)] =a^2/3[(1)+(1)] =2*a^2/3 so ans is D