The correct option is option D as 2cos²(x)cos²(x) simplifies as follows:
2cos²(x)cos²(x) = {3 + 4cos(2x) + cos(4x)} / 4
Simplification:
The given expression is : 2cos²(x)cos²(x)
The square identity for cosine is given by:
2cos²(x) -1 = cos(2x)
Thus,
2cos²(x) = {cos(2x) +1}
simplifying again,
cos²(x) = {cos(2x) +1}/2
Simplifying the above using squared identities:
2cos²(x)cos²(x) = {cos(2x) +1}cos²x
= {cos(2x) +1} {{cos(2x) +1}/2}
[tex]= \frac{\{cos(2x) +1\}^2}{2}\\\\=\frac{cos^2(2x)+2cos(2x)+1}{2}\\\\=\frac{\frac{cos(4x)+1}{2}+2cos(2x)+1}{2}\\\\=\frac{3+4cos(2x)+cos(4x)}{4}[/tex]
so,
2cos²(x)cos²(x) = {3 + 4cos(2x) + cos(4x)} / 4
Hence option D is correct.
Learn more about squared identities:
https://brainly.com/question/14613683?referrer=searchResults
