Front end shakes while braking

When going down hill at 50-75 mph and begin braking, the front end will shake. Shaking gets worse as number of braking attempts increases. Has reached a point of serious safety concern. Previously, rotors have been replaced, 4 new tires installed (old tires had strange wear pattern -- lot of cupping) alignment done. Never did solve problem. Has been a problem since buying the car with approx. 20,000 miles.
don't notice the problem when breaking on level ground or just driving without braking.