1. 两角和正切公式: tan[(x-y)+(y-z)]=[tan(x-y)+tan(y-z)]/[1-tan(x-y)tan(y-z)] tan(x-y)+tan(y-z) =tan(x-y+y-z)*[1-tan(x-y)tan(y-z)] =tan(x-z)*[1-tan(x-y)tan(y-z)] =tan(x-z)-tan(x-z)tan(x-y)tan(y-z) =-tan(z-x)+tan(z-x)tan(x-y)tan(y-z) tan(x-y)+tan(y-z)+tan(z-x)=tan(x-y)tan(y-z)tan(z-x) 2. 证明:∵x+y+z=nπ(n∈Z) ∴x+y=nπ-z ∴tan(x+y)=tan(nπ-z) 又∵tan(x+y)=(tan x + tan y)/(1-tanx tany) tan(nπ-z)=-tan z ∴tan x + tan y =-tanz+ tan x tan y tan z ∴tan x+tan y+tan z=tan x*tan y*tan z