Pas de deux is a dance duet in which two (typically male + female) dancers perform ballet step together. A strictly classical balletic pas de deux follows a fixed pattern: a supported adagio, a solo male variation, a solo female variation, and the final flashy coda.
The Tschaikovsky Pas de Deux is interesting for its music origin. The music is composed by Tchaikovsky, obviously. But actually it’s part of Swan Lake.
For the original production of Swan Lake in Moscow in 1877, Tschaikovsky composed a pas de deux for Act III at the request of Anna Sobeshchanskaya, a Bolshoi prima ballerina who was one of the first dancers to perform the lead role. Since it was composed later than the rest of the music, it was not included in the published score and was therefore not available to Marius Petipa when he choreographed his famous Swan Lake in St. Petersburg, in 1895. In its place, Petipa moved some music from Act I to Act III, and it is this piece that is now well-known as the Black Swan pas de deux. (The one with the 32 Fouettés)
Well over half a century later, the complete and original Swan Lake score was found, including an appendix with the lost pas de deux. Hearing of its historic discovery, George Balanchine asked for — and was granted — permission to use it for his own choreography. The result is an eight-minute display of ballet bravura and technique.
NYC Ballet’s Prima Ballerina Tiler Peck has the best version (I think) and she commented on her own performance of the female variation — 40s of excellence:
Full version here:
Reference
Wikipedia: Tschaikovsky Pas de Deux. https://en.wikipedia.org/wiki/Tschaikovsky_Pas_de_Deux#cite_note-:0-3
NYC Ballet: Tschaikovsky Pas de Deux. https://www.nycballet.com/discover/ballet-repertory/tschaikovsky-pas-de-deux/