sinα(α+π/6)=1/3则tan的平方(5/6π-α)=
问题描述：
sinα(α+π/6)=1/3则tan的平方(5/6π-α)=
答
如果是 sin(a+ π/6) =1/3的话
那么 sin(π-a-π/6)= sin(5/6π-a)= 1/3
cos^2 (5/6π-a)= 1-(1/3)^2 = 8/9
tan^2( 5/6π-a)= sin^2 ( 5/6π-a)/cos^2 ( 5/6π-a) = (1/9)/(8/9) = 1/8
答
sin(α+π/6)=1/3sin[π-(α+π/6)]=1/3sin(5/6π-α)=1/3sin²(5/6π-α)=1/9cos²(5/6π-α)=1-sin²(5/6π-α)=8/9tan²(5/6π-α)=sin²(5/6π-α)/cos²(5/6π-α)=1/9 / 8/9=1/8