To simplify the expression cot(x) * sin(x) * sin(cos(x)), we need to break down the components of the expression step by step.
1. **Identify the components**: The expression consists of three parts: cot(x), sin(x), and sin(cos(x)).
2. **Understand cotangent**: Recall that the cotangent function is the reciprocal of the tangent function. Hence, we can express cot(x) as:
cot(x) = 1/tan(x) = cos(x)/sin(x)3. **Substituting cotangent**: Substitute cot(x) in the original expression:
cot(x) * sin(x) * sin(cos(x)) = (cos(x)/sin(x)) * sin(x) * sin(cos(x))4. **Simplifying the expression**: Now, notice that sin(x) in the numerator cancels out with sin(x) in the denominator:
= cos(x) * sin(cos(x))5. **Final simplified expression**: Therefore, the simplified expression is:
cos(x) * sin(cos(x))This final result shows the relationship between the cotangent, sine function, and the cosine, simplified into a more manageable form.