They did, and there were multiple reasons for doing so.
You can look at the Apollo-Soyuz Test Project, which was the first joint US/Soviet space flight, which launched in the middle of the cold war (July, 1975) and featured a docking between ASTP's Apollo CM and Soyuz 19.
It was gereat fun, and stood as a symbol of detente between the USSR and US, and as a symbol of the end of the space race. Watching Alexei Leonov and Tom Stafford embrace on orbit was a moving moment, and a precursor of what we saw in the Shuttle-MIR program, and of course, in the ISS Program.
Of course, the reality of US -Russian or US-Soviet space cooperation was, and is, alot more beneficial and valuable than anything portrayed in a fictional horror story about spaceflight, and silliness.
Before you mis-interpret this as being another example of people's meanness, how about those questions you've mentioned, and which need to be answered.
That's what we're about here: Answering peoples questions and addressing their doubts.
Edited by MID, 05 May 2012 - 07:55 PM.