Question

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

Answer 1

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°