To find the value of sin(4x) cos(4x) cot(4x), we can start by using some trigonometric identities.
First, we know that:
- cot(θ) = cos(θ) / sin(θ)
So we can rewrite cot(4x) as:
cot(4x) = cos(4x) / sin(4x)
Now substituting this into our expression:
sin(4x) cos(4x) cot(4x) = sin(4x) cos(4x) (cos(4x) / sin(4x))
The sin(4x) in the numerator and denominator will cancel each other out (provided that sin(4x) is not equal to zero). So we are left with:
cos^2(4x)
Thus, the final value of sin(4x) cos(4x) cot(4x) simplifies to:
cos^2(4x)
In summary, the process involves using the cotangent definition to simplify the original expression effectively.