tana=7,tanβ=3,a,β为锐角,求证 a+2β=5π/4

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tana=7,tanβ=3,a,β为锐角,求证a+2β=5π/4tana=7,tanβ=3,a,β为锐角,求证a+2β=5π/4tana=7,tanβ=3,a,β为锐角,求证a+2β=5π/4∵tan

tana=7,tanβ=3,a,β为锐角,求证 a+2β=5π/4
tana=7,tanβ=3,a,β为锐角,求证 a+2β=5π/4

tana=7,tanβ=3,a,β为锐角,求证 a+2β=5π/4
∵tanβ=3
∴tan(2β)=2tanβ/(1-tan²β)=-3/4
tan(α+2β)=[tanα+tan(2β)]/[1-tanα·tan(2β)]
tan(α+2β)=(7-3/4)/(1+7×3/4)
tan(α+2β)=(25/4)/(25/4)
tan(α+2β)=1
∵0<β<π/2
∴0<2β<π
∵0<α<π/2
∴0<α+2β<3π/2
tan(α+2β)=1,0<α+2β<3π/2
∴α+2β=5π/4

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