化简:(1/tan(a/2)-tana/2)(1+tanatana/2)
问题描述：
化简:(1/tan(a/2)-tana/2)(1+tanatana/2)
答
(1/tanA/2-tanA/2)(1+tanAtanA/2)
=[(1-tan²A/2)/tanA/2][1+2tan²A/2/(1-tan²A/2)]
=[(1-tan²A/2)/tanA/2][(1+tan²A/2)/(1-tan²A/2)]
=(1+tan²A/2)/tanA/2
=sec²A/2/tanA/2
=2/sinA
=2cscA
答
设a=A则(1/tanA/2-tanA/2)(1+tanAtanA/2)=[(1-tan²A/2)/tanA/2][1+2tan²A/2/(1-tan²A/2)]=[(1-tan²A/2)/tanA/2][(1+tan²A/2)/(1-tan²A/2)]=(1+tan²A/2)/tanA/2=sec²A/2/tan...