Question

①已知sinα-cosβ=1/2,cosα-sinβ=1/3,则sin（α+β)=

Answer 1

1.(sinα-cosβ)^2+(cosα-sinβ)^2=2-2sinαcosβ-2cosαsinβ=2-2sin（α+β)=(1/2)^2+(1/3)^2

=>sin（α+β)=59/72

2.tan(A+B)=tan(π/4+kπ)=1

=>(tanA+tanB)/(1-tanAtanB)=1

=>tanA+tanB+tanAtanB=1

=>1+tanA+tanB+tanAtanB=1+1=2

=> （1+tanA)(1+tanB)=2