You have a couple of problems doing this. First, a washer uses an open top standpipe. The hooked end of the washer drain hose just hooks over this. In other words, the hose is not solidly attached to the drain. Secondly, a washer requires a 2" drain because a washer ejects a relatively large amount of water in a short period of time. The waste water is pumped out at a faster rate than you will get out of opening a tap. Your sink has a 1-1/2" drain. You may not think this is much difference, but if you recall how to figure the area of a circle, you can see that there is a huge difference in area between 1-1/2" and 2" diameter circles. Now, if you can hook the drain hose over the sink so that the water flows into the sink, perhaps the sink will hold enough water so that the smaller sink drain will work. This is not the proper way to do it, but if there is no other way, it might work.