If `|[sin2x,cos^2x,cos4x],[cos^2x,cos2x,sin^2x],[cos^4x,sin^2x,sin2x]|=a_0+a_1 (sinx)+a_2(sin^2x)+....+a_n(sin^n x)` then the value of `a_0` is-

3-2cos x-4sin x-cos2x+sin2x=0

If f(x)=[[1+sin^2x,cos^2x,4sin2x],[sin^2x,1+cos^2x,4sin2x],[sin^2x,cos^2x,1+4sin2x]] what is the maximum value of f(x).

If the determinant |(cos2x,sin^2 x,cos 4x),(sin^2 x,cos 2x,cos^2 x),(cos 4x,cos^2 x,cos 2x)| is expanded in powers of sin x , then the constant term is

If the determinant |(cos2x,sin^2 x,cos 4x),(sin^2 x,cos 2x,cos^2 x),(cos 4x,cos^2 x,cos 2x)| is expanded in powers of sin x, then the constant term is

If f(x)=|(1+sin^(2)x,cos^(2)x,4sin2x),(sin^(2)x,1+cos^(2)x,4sin2x),(sin^(2)x,cos^(2)x,1+4sin2x)| then the maximum value of f(x) is

If f(x)=|{:(5+sin^2x,cos^2x,4sin2x),(sin^2x,5+cos^2x,4sin2x),(sin^2x,cos^2x,5+4sin2x):}| then evaluate

Let f(x)=|[1+sin ^2 x, cos ^2 x , 4 sin 2 x],[ sin ^2 x ,1+cos ^2 x , 4 sin 2 x],[ sin ^2 x , cos ^2 x , 1+4 sin 2 x]| , the maximum value of f(x) is