已知阿尔发,贝塔为锐角,tan阿尔法＝7分之1,sin贝塔＝10分之根号10,求阿尔法＋2贝塔的值

α、β为锐角,
tanα=1/7,
sinβ=√10/10
cosβ=√{1-(√10/10)²} = 3√10/10
tanβ = sinβ/cosβ=1/3
tan2β = 2*(1/3)/{1-(1/3)²} = 3/4,2β也为锐角
α+2β ＜180°
tan(α+2β) = (tanα+tan2β) /(1-tanαtanα2β) = (1/7+3/4)/(1-1/7*3/4) = 25/25=1
α+2β=45°