Question

三角方程tan(x+π/4) - tan(x- π/4)=4,求 x之值

Answer 1

tan(x+π/4) - tan(x- π/4)=4

令t=x-π/4

则t+π/2=x+ π/4

则

tan(t+π/2) - tan(t)=4

cot(-t) - tan(t)=4

-1/tan(t)-tan(t)=4

tan²(t)-4tan(t)+1=0

tan(t)=2±√3

则

t=5π/12+2kπ或π/12+2kπ

x=t+π/4=2π/3+2kπ或π/3+2kπ,k∈Z