I guess for 22 fill 1/2 you mean 22+1/2=45/2 and so tan45/2=x and cos135/2=??.
cos135/2=cos(180-45)/2=cos(90-45/2)=sin45/2. In triangle ABC, if B is 90 degrees, and A is 45/2 degrees, then BC/AB=tan45/2=x/1. By Pythagoras AC^2=AB^2+BC^2=1+x^2. So sin45/2=x/sqrt(1+x^2)=cos135/2. So the answer, without evaluating x, is x/sqrt(1+x^2).
[However, x can be evaluated because we know sin45=cos45=1/sqrt(2) and tan45=1. From these we can work out that tan45/2=sqrt(2)-1=x.]