Let a = x, since the letters x is usually a variable, and 
letters a and b are usually constants.  Then b = 90°-a = 90°-x 

I will approach it from a calculus standpoint.


y = cos(x)cos(90-x)

y = cos(x)sin(x)





Setting that = 0

Cos(2x)=0

2x = 90°, 270°, 450°, etc.

x = 45°, 135°, 225°, etc.

Substituting these in 

y = cos(x)sin(x)

y = cos(45°)sin(45°) = 

y = cos(135°)sin(135°) = 

y = cos(225°)sin(225°) = 

etc.

So the maximum value is  and the minimum value is .

Edwin