已知A B为锐角,且(1+tanA/2)(1+tanB/2)=2,则tanAtanB=?
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已知A B为锐角,且(1+tanA/2)(1+tanB/2)=2,则tanAtanB=?
已知A B为锐角,且(1+tanA/2)(1+tanB/2)=2,则tanAtanB=?
已知A B为锐角,且(1+tanA/2)(1+tanB/2)=2,则tanAtanB=?
(1+tanA/2)(1+tanB/2)=2
1+tanA/2+tanB/2+tanA/2tanB/2=2
tanA/2+tanB/2=1-tanA/2tanB/2
tan(A/2+B/2)=1
∴A/2+B/2=π/4
∴A+B=π/2
tanAtanB=tanBtan(π/2-B)=tanBcotB=1