Answer:
![y=-(2)/(√(4-\pi^2))x+Undefined]()
Step-by-step explanation:
Given the function:

First, determine the tangent point by evaluating f(x) at x=π/2:
![f((\pi)/(2))=\cos^(-1)((\pi)/(2))=Undefined]()
Note: f(π/2) is undefined because the domain of arccosine is (-1,1).
The tangent point is:
![((\pi)/(2),Undefined)]()
Next, find the slope of the tangent line. Begin by finding the derivative of f(x):
By the rules of derivative:

At x=π/2, find the value of the derivative:

Thus, the equation of the tangent line is:
![y=-(2)/(√(4-\pi^2))x+Undefined]()