若&,@均为锐角且tan&=1/2,tan@=1/3,则&+@=

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若&,@均为锐角且tan&=1/2,tan@=1/3,则&+@=
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若&,@均为锐角且tan&=1/2,tan@=1/3,则&+@=
若&,@均为锐角且tan&=1/2,tan@=1/3,则&+@=

若&,@均为锐角且tan&=1/2,tan@=1/3,则&+@=
tan(A+B)
=(tanA+tanB)/(1-tanAtanB)
=(1/2+1/3)/(1-1/2 *1/3)
=(5/6)/(5/6)
=1
&+@=A+B=π/4


&,@均为锐角
∴ 0<&+@<π
∵ tan&=1/2,tan@=1/3
∴ tan(&+@)
= (tan&+tan@)/(1-tan&tan@t)
=(1/2+1/3)/[1-(1/2)*(1/3)]
=(5/6)/(5/6)
=1
∴ &+@=π/4