The images are the first known footage of tigers in the remote mountains of Bhutan and the first hard evidence that tigers are capable of living at that altitude.
This find was made in close collaboration with Bhutan Ministry of Agriculture and Forests, with help and guidance from forest guard Phup Tshering.
"The fact they can live here is just so important, for tigers in the wild, for their future," said Mr Buchanan, on seeing the footage for the first time.
The large male tiger, sighted at an altitude of 4,100m is recorded scent-marking, confirming that the tiger pair are living within their own territory, and not just passing through.
The female tiger, sighted at the same altitude, can also be seen to be lactating, strongly suggesting the tigers are breeding at that altitude.
Further footage shows tigers living lower at an altitude of 3000m.
The discovery, which is broadcast this week as part of the BBC One programme Lost Land of the Tiger was made by the same BBC team that discovered a new species of giant rat living on the slopes of a remote volcano deep inside the jungle of Papua New Guinea.
The highest living tigers in the world endure snowy conditions
Dr Rabinowitz and the BBC team are not revealing the exact location of the tigers, in order to prevent them being found by poachers.
Tigers used to roam across Asia, now only pockets remain. There are estimated to be as few as 3,000 left in the wild, due to poaching and habitat loss.
The discovery of tigers living at altitude in Bhutan could be crucial to one scheme proposed to help save the species from extinction.
Known as a "tiger corridor", the idea is to connect up many of these surviving isolated and fragmented groups.
That would allow individual tigers to move between populations, allowing them to breed more widely, bolstering the genetic diversity of those surviving.
It would also offer some tigers sanctuary from human towns and villages and the increasing pressures they bring.
The Tiger Corridor Initiative,
promoted by the conservation organisation Panthera, hopes one such major corridor could extend along the foothills of the Himalayas from Nepal into Bhutan and northern India, then through to Myanmar, stretching across 2000km with an area of 120,000 sq km. The ambition would then be to connect it to another corridor spanning Thailand, Laos, Cambodia, terminating in Malaysia.
"The significance of finding tigers living so high in Bhutan is that it means that huge areas of Himalayas, that people didn't think were natural places for tigers to live, can now be included in the tiger corridor," says Jonny Keeling, a BBC producer who helped track and film the big cats.
"Bhutan could act as tiger nursery from which tigers could breed safely and spread out to re-populate forests of some of the surrounding countries."
Lost Land of the Tiger will be broadcast on BBC One at 21.00BST on Tuesday 21st, Wednesday 22nd and Thursday 23rd September.
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