数学三角比的诱导公式题目

2sin2(α+β)是sin(α+β)的平方的2倍吧?
tanα+tanβ=5,tanα*tanβ=6,tan(α+β)=(tanα+tanβ)/(1-tanα*tanβ)=-1.
[sec(α+β)]^2=1+[tan(α+β)]^2=2,[cos(α+β)]^2=1/[sec(α+β)]^2=1/2.
2[sin(α+β)]^2-3sin(α+β)×cos(α+β)+[cos(α+β)]^2
=[cos(α+β)]^2*{2[tan(α+β)]^2-3tan(α+β)+1}
=3.