Re: When ?? try 1970 when Marine SSB Radio became std...
The question was "When did Bose enter the headphone Market?" so your answer "try 1970..." is not relevant, nor is any reference to SSB and Plessey.
I worked in the pro-audio business from about 1970, on and off for about 9 years and then full-time until the end of the 90s.
In all that time I never saw a pair of Bose headphones. Sennheiser, AKG and Beyer were the dominant pro manufacturers with Koss dominating the domestic hifi side until Sony and Audio-Technica seemed to push them aside. There were other brands, but mostly irrelevant
According to the Bose website and it's official time-line, Dr Bose conceived the mathematics for noise cancelling-headphones while on a SwissAir flight in 1976. Its prototypes appeared ten years later in 1986 but they were not in production until 1989, and then not available in the consumer space until 2000.
It is therefore disingenuous (and bogus) for Bose claim that they have been developing noise-cancelling headphones for 40 years,
Although I can't immediately find proof, I'm convinced that RACAL were using an identical system of 'anti-noise' at the same time that Bose claim to have invented it. (Bose quote: "ANR is a technique to reduce unwanted noise by introducing a second sound source that destructively interferes with the unwanted noise," ). In the claim against Beats, the earliest patent is from 2004 and appears to introduce the digital domain into the second souce sound - something that should be fairly obvious to anyone working in that area.
Also, your claim that "..everyone came and used it, there are USD $30 Japanese headphones, and there are USD $500 German headphones, all licensed and blessed by Bose." is contradicted by Bose themselves here:
"Our patents cover our unique approach to active noise cancellation," Carolyn Cinotti, director of public relations at Bose.
"Other companies may have their own unique approach. We don't license our technology to other headphone manufacturers."