sinb=sin(a+b-a)=sin(a+b)cosa-cos(a+b)sina=2cos(a+b)sina sin(a+b)cosa=3cos(a+b)sina
tan(α+β）=3tanα
tan(a+b)=3tana
经变换得
tanb=2tana/(1+3tana^2)
2/(1/tana+3tana) 由均值不等式可得1/tana+3tana>=2根号3
最大值为2/(2根号3）=根号3/3