Question

如何证明cot(1/2A)-tan(1/2A)=2cot(A)

Answer 1

左边=cos(A/2)/sin(A/2)-sin(A/2)/cos(A/2)

=[cos²(A/2)-sin²(A/2)]/sin(A/2)cos(A/2)

=2[cos²(A/2)-sin²(A/2)]/[2sin(A/2)cos(A/2)]

=2cosA/sinA

=2cotA=右边

命题得证