求证tan(A/2)-{1/(tanA/2)}=-2/tanA

问题描述:

求证tan(A/2)-{1/(tanA/2)}=-2/tanA
写出详细过程,谢谢

tanA=2tan(A/2)/[1-(tan(A/2))^2]
-2/tanA
=-2*[1-(tan(A/2))^2]/[2tan(A/2)]
=[(tan(A/2))^2-1]/(tanA/2)
tan(A/2)-1/(tanA/2)
=[(tan(A/2))^2-1]/(tanA/2)
所以tan(A/2)-1/(tanA/2)=-2/tanA