已知tan(派－阿拉法)=1/2,sin贝他＝3/5,（贝他）属于（派/2,派）,求tan(2阿拉法－贝他)的值

Question

已知tan(派－阿拉法)=1/2,sin贝他＝3/5,（贝他）属于（派/2,派）,求tan(2阿拉法－贝他)的值

Answer 1

tan(π－α)=-tanα=1/2 tanα=-1/2
tan2α=(2tanα)/[1-(tanα)^2]=-4/3
sinβ=3/5 β∈[ π/2,π]
cosβ=-4/5
tanβ=sinβ/cosβ=-3/4
tan(2α-β)=(tan2α-tanβ)/(1+tan2αtanβ)
=-7/24