已知tan(派加a)=2,tan(a加被他)=5,且a大于0小于二分之派,a加被他大于派小于二分之3派,求sin被他的值 急

题目

已知tan(派加a)=2,tan(a加被他)=5,且a大于0小于二分之派,a加被他大于派小于二分之3派,求sin被他的值 急

答案

tan(π+α）=2；tanα=-2;
tan(α+β)=5;(tanα+tanβ)/（1-tanαtanβ）=5,tanβ=-7/9;
(sinβ)^2+(cosβ)^2=1,(sinβ)^2=(tanβ)^2/1+(tanβ)^2=49/130;
π/2≤β≤π;
sinβ=7/√130