I have the function $$ g(x,y,t)=\frac{(8x^2y^2+f(x,y,t)+\cos(2t))(8x^2y^2(1+(x+y)^2)+(x+y)^2(f(x,y,t)-\cos(t)))}{64x^4y^4(1+(x+y)^2)} $$ with $$ f(x,y,t) = 1+2x^2+2y^2-4xy\cos(2t)-2(x+y)\sin(2t). $$ Is is possible to analytically prove $g(x,y,t)\ge1$? I have numerically checked it for many values of variables (x,y,t). Any suggestion will be helpful.