β为锐角.且α,β满足4tan*α/2=1-tan^2*α/2.3sinβ=sin(2α+β)求α+β
问题描述：
β为锐角.且α,β满足4tan*α/2=1-tan^2*α/2.3sinβ=sin(2α+β)求α+β
答
(1).由正切的半角公式知2tana=1.===>tana=1/2.===>sin2a=4/5,cos2a=3/5.(2)3sinb=sin(2a+b)=sin2acosb+cos2asinb=(4/5)cosb+(3/5)sinb.===>tanb=1/3.(3)tan(a+b)=[tana+tanb]/(1-tanatanb)=1.===>a+b=π/4.