Use an addition or subtraction formula to simplify the expression:

tan(2−u)=cot(f(u)).

tan(2−u)=cot(f(u))

take cot^-1 of both sides , (take the inverse cotangent)
cot^-1 [tan(2-u) ] = cot^-1 [cot(f(u)) \
cot^-1 [tan(2-u) ] = f(u)
cot^-1 [ cot(1/(2-u) ) ] = f(u)

1/(2-u) = f(u) , u ≠ 2

Use an addition or subtraction formula to simplify the expression:

tan(π/2−u)=cot(f(u)).

To simplify the expression tan(2−u) = cot(f(u)), we'll use the addition/subtraction formula for tangent and cotangent.

The addition/subtraction formula for tangent states that:
tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))

And the addition/subtraction formula for cotangent states that:
cot(a - b) = (cot(a)cot(b) - 1) / (cot(a) + cot(b))

So, we'll rewrite the given expression using the formula:

tan(2 - u) = cot(f(u))
(tan(2) - tan(u)) / (1 + tan(2)tan(u)) = (cot(f(u))cot(u) - 1) / (cot(f(u)) + cot(u))

Since the angles 2 and u are constant, let's denote them as A and B respectively. Similarly, let's denote f(u) as C.

(tan(A) - tan(B)) / (1 + tan(A)tan(B)) = (cot(C)cot(B) - 1) / (cot(C) + cot(B))

Now we can simplify the expression by substituting the given values.

To simplify the expression tan(2-u) = cot(f(u)), we need to make use of the addition or subtraction formulas for tangent and cotangent functions.

The tangent and cotangent formulas state:
1. tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a) * tan(b))
2. cot(a + b) = (cot(a) * cot(b) - 1) / (cot(b) + cot(a))

Let's apply these formulas step by step:

1. Start with the given expression: tan(2-u) = cot(f(u))

2. By comparing the formulas, we can see that the angle (2 - u) is equivalent to (f(u)) + (f(u)). So we can rewrite the expression as tan((f(u)) + (f(u))) = cot(f(u)).

3. Applying the tangent addition formula, we get:
(tan(f(u)) + tan(f(u))) / (1 - tan(f(u)) * tan(f(u))) = cot(f(u))

4. By simplifying the numerator, we have:
2 * tan(f(u)) / (1 - (tan(f(u)))^2) = cot(f(u))

5. Notice that (tan(f(u)))^2 is the same as 1 + (cot(f(u)))^2 (from the Pythagorean identity). Substituting this in the denominator:
2 * tan(f(u)) / (1 - (1 + (cot(f(u)))^2)) = cot(f(u))

6. Simplifying further:
2 * tan(f(u)) / (-cot(f(u))^2) = cot(f(u))

7. Multiplying both sides of the equation by (-cot(f(u)))^2, we have:
2 * tan(f(u)) = -cot(f(u))

8. Dividing both sides by 2, we get:
tan(f(u)) = -cot(f(u))

9. Finally, we can rewrite this as:
tan(f(u)) + cot(f(u)) = 0

Therefore, the simplified expression is tan(f(u)) + cot(f(u)) = 0.