Find the equations of sides of the triangle having (4,-1) as a vertex, if the lines x-1=0 and x-y-1=0 are the equations of two internal bisectors of its angles.

Dear student 

If 2 lines are symmetric about any  x=a,  then their slopes will be negative of each other. Suppose, one equation is known to us as  y=mx+c , then the other equation will be  y=−mx+d 
If  y=x+k  is the symmetric axis, then the product of slopes should be  1 . Example, the pair of lines  y=4x+c  and  y=0.25x+d , will be symmetric about some  y=x+k . In other words, the coefficients of x and y get exchanged.
Once, the above points are clear, all that is left is to start with some line, say AB and use the constraints like passing through A, concurrency of AC, CB and  y=x−1 , and concurrency of AB, BC and x = 1.