题目

若sinQ+cosQ=√2,则tan(Q+π/3)的值是?

提问时间：2021-03-05

答案

∵sinQ+cosQ=√2
∴(√2)sin(Q+π/4)=√2
∴sin(Q+π/4)=1
∴Q+π/4=π/2+2kπ(k∈Z)
∴Q=π/4+2kπ(k∈Z)
∴tanQ=tan(π/4+2kπ)=tan(π/4)=1
∴tan(Q+π/3)
=[tanQ+tan(π/3)]/[1-tanQtan(π/3)]
=(1+√3)/(1-√3)
=(1+√3)^2/[(1-√3)(1+√3)]
=(1+2√3+3)/(1-3)
=(4+2√3)/(-2)
=-(2+√3).