Question

化简：sin2a(1+tanatan乘a/2)=?已知tan(a减被他)=1/2,tan(a+被他)=2,则tan2被他

Answer 1

1、sin2α（1+tanα*tanα/2)={1+(tanα/2)^2/[1-(tanα/2)^2]}sin2α=2sin2a/cosa=2sina,

tanα=2tanα/2/[1-(tanα/2)^2]

tan2β=tan[(α+β）-tan(α-β)]/[1+tan(α+β)tan(α-β)]

=(2-1/2)]/[1+2*1/2)=3/4.