As you know

The value of cos(x) lies between (-1 & 1).

So put any value of cos(x) between (-1) and (1) in cos(**cos(x)**).

cos(-1) = cos(1) as [cos(-x) = cos(x)]

cos(0) = 1

It is clear from the above value that the value of cos(cos(x)) is between **"cos(1)" and "1".**

**Also, **cos(x) is a decreasing function in 0° and 90°. so as the maximum value of cos(x) will be at 0° and minimum at 1° in this question.