Solve 2 tan θ = 2 cot θ for all values of θ if θ is measured in degrees.

2tanθ = 2cotθ

tanθ = cotθ

tanθ = 1 /tanθ

tan²θ = 1

tanθ = ±1

if tanθ = 1

θ = 45° + nπ  (π = 180° , n is a natural number)

if tanθ = -1

θ = 135° + nπ

f(x) = (x – 8)(x – 4)(x – 4)(x + 3)

Step-by-step explanation:

A polynomial function with roots has the following format:

In which a is the leading coefficient.

In this problem, we have that:

Leading coefficient 1, so

roots -3 and 8 with multiplicity 1, so .

root 4 with multiplicity 2, so

So the correct answer is:

f(x) = (x – 8)(x – 4)(x – 4)(x + 3)