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Geometrical proof that tan x tan y + tan y tan z + tan z tan x= 1 when x + y + z = 90°
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H being the orthocentre of a triangle ABC, we may call the angles HAC, HBA, HCB = x, y, z respectively, for their sum is 90°.Now tan x tan z = ∴ tan x tan z + tan z tan y + tan x tan y = 1.
Title: Geometrical proof that tan x tan y + tan y tan z + tan z tan x= 1 when x + y + z = 90°
Description:
H being the orthocentre of a triangle ABC, we may call the angles HAC, HBA, HCB = x, y, z respectively, for their sum is 90°.
Now tan x tan z = ∴ tan x tan z + tan z tan y + tan x tan y = 1.
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