For the given domain, you will find that the maximum and minimum values occur at the endpoints, that is, at x = 0 degrees and x = 90 degrees respectively.
As Mr. F has said : subs. the endpoints of the domain
When x = 0 --------------------> cos x = 1 and sin x = 0
When x = 90 degrees -------> cos x = 0 and sin x = 1
So, in this case, the maximum value of sin and cos is 1 and minimum value is 0.
When you want to find the maximum value of , you make the value of the numerator as big as possible and the denominator as small as possible.
Because the max. value of cos is 1, then you take x = 0 to optimize the numerator. For x = 0, the value of sin = 0, so you'll get :
To find the min. value, you make the numerator as small as possible and the denominator as big as possible. Give it a try