tan(x-派/3)=-根号3/5,tanx等于多少?

题目

tan(x-派/3)=-根号3/5,tanx等于多少?

答案

tan(x-π/3)
=(tanx-tanπ/3)/(1+tanxtanπ/3)
=(tanx-√3)/(1+√3tanx)=-√3/5
5(tanx-√3)=-√3(1+√3tanx)
5tanx-5√3=-√3-3tanx
8tanx=4√3
tanx=√3/2