Step 1. The expression that we have is:
[tex]cos^2(5x)[/tex]
and we need to find the equivalent expression.
Step 2. The trigonometric identity we will use to solve this problem is:
[tex]cos^2A=1-sin^2A[/tex]
In this case:
[tex]A=5x[/tex]
Step 3. Applying the trigonometric identity to our expression, substituting 5x in the place of A:
[tex]cos^2(5x)=\boxed{1-sin^2(5x)}[/tex]
This is shown in option d).
Answer:
[tex]\boxed{d)\text{ }1-s\imaginaryI n^2(5x)}[/tex]
