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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°

Published online by Cambridge University Press:  31 October 2008

G. E. Crawford
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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.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 20 , April 1916 , pp. 237 - 238
Copyright
Copyright © Edinburgh Mathematical Society 1916