Question

已知α,β∈(0,π/2),tanα=1/7,sinβ=1/√10,求sin(α+β)的值

Answer 1

sinb=1/√10

cosb=3/√10

tanb=1/3

tan(a+b)=(tana+tanb)/(1-tanatanb)

=(1/3+1/7)/(1-1/21)

=1/2

cos(a+b)^2=1/[1+tan(a+b)^2]=4/5

sin(a+b)^2=1/5

sin(a+b)=1/√5