If the maximum and minimum values of the determinant
`|(1 + sin^(2)x,cos^(2) x,sin 2x),(sin^(2) x,1 + cos^(2) x,sin 2x),(sin^(2) x,cos^(2) x,1 + sin 2x)|` are `alpha and beta`, then

If the maximum and minimum values of the determinant |(1+sin^(2)x,cos^(2)x,sin2x),(sin^(2)x,1+cos^(2)x,sin2x),(sin^(2)x,cos^(2)x,1+sin2x)| are alpha and beta respectively, then alpha+2beta is equal to

If the maximum and minimum values of the determinant |(1+sin^(2)x,cos^(2)x,sin2x),(sin^(2)x,1+cos^(2)x,sin2x),(sin^(2)x,cos^(2)x,1+sin2x)| are alpha and beta respectively, then alpha+2beta is equal to

If maximum and minimum values of the determinant |{:(1 + cos^(2)x , sin^(2) x, cos 2x),(cos^(2) x , 1 + sin^(2)x, cos 2x),(cos^(2) x , sin^(2) x , 1 + cos 2 x):}| are alpha and beta then

If maximum and minimum values of the determinant |{:(1+sin^2x,cos^2x,sin2x),(sin^2x,1+cos^2x,sin2x),(sin^2x,cos^2x,1+sin2x):}| are alpha and beta then show that (alpha^(2n)-beta^(2n)) is always an even integer for n in N .

Find maximum value of 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):}| .

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

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)= |{:(,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

The maximum value of f(x)=|(sin^(2)x,1+cos^(2)x,cos2x),(1+sin^(2)x,cos^(2)x,cos2x),(sin^(2)x,cos^(2)x,sin2x)|,x inR is :