Question

若sinα+cosα=根号2,则tan(α+π/3)=?

Answer 1

sinα+cosα=根号2(根号2/2sinα+根号2/2cosα)
=根号2sin(α+π/4)
=根号2
所以sin(α+π/4)=1，α=π/4+2kπ
tan(α+π/3)=tan(π/4+2kπ+π/3)
=(tanπ/4+tanπ/3)/(1-tanπ/4tanπ/3)
=(1+根号3)/（1-根号3）

Answer 2

(sinα+cosα)²=1+sin2α=2
sin2α=1==>2α=π/2+2kπ
α=π/4+kπ
tanα=1
tan(α+π/3)=[1+√3)]/[1-√3]=[1+√3)]²/[1-√3][1+√3)]= - 2-√3