若sinα+cosα=√2,则tanα+(1/tanα)=

问题描述:

若sinα+cosα=√2,则tanα+(1/tanα)=

用x代替
sinx+cosx
=√2(√2/2*sinx+√2/2cosx)
=√2(sinxcosπ/4+cosxsinπ/4)
=√2sin(x+π/4)=√2
sin(x+π/4)=1
x+π/4=2kπ+π/2
x=2kπ+π/4
则tanx=tan(2kπ+π/4)=tanπ/4=1
所以原式=1+1=2