Final answer:
Simplifying the given equation cot(-x) ⋅ cos(-x) ⋅ sin(-x) = -1, we find that there is no solution for f(x) in this equation as cosine squared cannot be negative.
Step-by-step explanation:
To find f(x) in the equation cot(-x) ⋅ cos(-x) ⋅ sin(-x) = -1, we need to simplify the expression and solve for x. First, we use the properties of trigonometric functions to rewrite the expression in terms of positive angles. The cot(-x) can be written as cot(x), and cos(-x) and sin(-x) can be written as cos(x) and sin(x) respectively. Substituting these values, we get cot(x) ⋅ cos(x) ⋅ sin(x) = -1.
Next, we can rewrite cot(x) as cos(x)/sin(x). Substituting this, we get (cos(x)/sin(x)) ⋅ cos(x) ⋅ sin(x) = -1. Simplifying further, we get cos²(x) = -1. However, cosine squared cannot be negative, so there is no solution for f(x) in this equation.