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Tan x = Tan (45 - y) = (Tan 45 - Tan y)/(1 + Tan 45 Tan y)
= (1 - Tan y)/(1 + tan y)
(1 + Tan x)(1 + Tan y)
= (1 + (1 - Tan y)/(1 + Tan y)) (1 + Tan y)
= (1 + Tan y) + (1 - Tan y)
= 1 + 1
= 2