Using the Pythagoreum Identity

There's many ways of doing this one. 

The most direct method, at least to me, is the following: 

1 - (11/61)^2 = 1 - (121/3721) --> (1/1) - (121/3721) we multiply the denominators to get 3721. then cross multiply multiply to get the numerator.3721 * 1 = 3721 and 1 * -121 = -121. Thus, for the numerator we get: 3721 -121 = 3600. 

The answer is therefore, 3600/3721

Hope that makes sense.