The maximum and minimum value of cos(x) is 1 and -1. And cos(cosx) = at x = 0 is cos(1) , it is minimum value . Here the cos function decreases from 0 to 90 degree, so it has smooth relations between angles .

Answer is 0 to π because it like a cos^-1y vs cos x garph whose end points are 0 toπ

Maximum and Minimum Value of cos(cosx)
Cosine function ranges from -1 to 1. When applying cosine function to another cosine function, the values will be constrained between -1 and 1.

Maximum Value:
- The maximum value of cos(cosx) is 1.
- This occurs when the inner cosine function, cosx, equals 0.
- Since the range of cosx is between -1 and 1, the maximum value of cos(cosx) is 1.

Minimum Value:
- The minimum value of cos(cosx) is cos(1).
- This occurs when the inner cosine function, cosx, equals ±1.
- The value of cos(1) is approximately 0.5403, which is the minimum value of cos(cosx).
In conclusion, the maximum value of cos(cosx) is 1 and the minimum value is approximately 0.5403. The values are derived from the range of the cosine function and its application to another cosine function.