若&,@均为锐角且tan&=1/2,tan@=1/3,则&+@=

来源:学生作业学帮网 编辑:学帮网 时间:2024/06/02 04:29:25

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