Career
He served as private secretary to the Minister of Trade 1946-1947, state secretary to the Minister of Trade in 1947, and state secretary to the Minister of Industry 1947-1951. On 29 June 1951, he was made acting Minister of Industry when Jens Evensen took leave of absence. His tenure was short, however, as the second cabinet of Einar Gerhardsen resigned on 19 November the same year.
Drogseth was a mining engineer by profession, and after his resignation from the government he served as manager of the mining company Norsk Bergverk until 1963.