设tana=1/7,tanβ=1/3,且a,β都是锐角,求证:a+2β=π/4
问题描述:
设tana=1/7,tanβ=1/3,且a,β都是锐角,求证:a+2β=π/4
答
tan(a+2β)=(tana+tan2β)/(1-tanatan2β)
tan2β=2tanβ/(1-tan^2β)=2/3/8/9=3/4
tan(a+2β)=(tana+tan2β)/(1-tanatan2β)
=(1/7+3/4)/(1-1/7*3/4)=1
a+2β=π/4