tanα=1/7 tanβ= 1/3,且α、β均为锐角,求α+2β的值.(请写明具体步骤)

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tanα=1/7 tanβ= 1/3,且α、β均为锐角,求α+2β的值.(请写明具体步骤)
tanα=1/7 tanβ= 1/3,且α、β均为锐角,求α+2β的值.(请写明具体步骤)

tanα=1/7 tanβ= 1/3,且α、β均为锐角,求α+2β的值.(请写明具体步骤)
tan2β=2tanβ/1-tan^2β
=(2/3)/(1-1/9)
=3/4
tan(α+2β)=(1/7+3/4)/(1-3/28)
=(25/28)/(25/28)
=1
因为tan2β=3/4>0
所以0

tan2b=2tanb/1-tan^2b=2/3/8/9=2/3*9/8=3/4
tan(a+2b)=1/7+3/4/1-3/28
=25/28/25/28=1
tan(a+2b)=1
a+2b=pi/4