To find the value of sin(4x) cos(4x) cot(4x), let’s start by breaking down what each of these terms means and how they relate to each other mathematically.
1. **Understanding the Terms**:
- sin(4x): This represents the sine of an angle measured in radians or degrees, in this case, 4 times x.
- cos(4x): This is the cosine of the same angle, 4 times x.
- cot(4x): The cotangent function is the reciprocal of the tangent function. Thus, cot(4x) = 1/tan(4x). Since tan(4x) = sin(4x)/cos(4x), we can express cot(4x) as cos(4x) / sin(4x).
2. **Using Identities**: Now, let’s substitute cot(4x) in our expression:
sin(4x) cos(4x) cot(4x) = sin(4x) cos(4x) (cos(4x)/sin(4x))
3. **Simplifying the Expression**: This simplification leads us to:
sin(4x) cos(4x) cot(4x) = cos2(4x)
4. **Final Value**: Therefore, we conclude that:
sin(4x) cos(4x) cot(4x) = cos2(4x)
This result means that the value of sin(4x) cos(4x) cot(4x) is equal to the square of the cosine of 4x. Depending on what you’re trying to find out, you can then compute this value given a specific angle for x.
In summary:
- sin(4x) cos(4x) cot(4x) = cos2(4x)