The given question is
[tex] 2sin^2 x cos^2 x [/tex]
Multiplying and divide by 2
[tex] \frac{4sin^2 x cos^2 x}{2} =\frac{(2 sinx cos x})^2{2}=\frac{sin^2(2x)}{2} [/tex]
Again multiplying and dividing by 2
[tex] \frac{2sin^2(2x)}{4} [/tex]
And
[tex] 2 sin^2(2x)=1-cos(4x) [/tex]
So we will get
[tex] \frac{1-cos(4x)}{4} [/tex]
Correct option is D
