Question

如何证明 cosecA + cotA= cot(A/2)

Answer 1

左边=1/sinA+cosA/sinA

=(1+cosA)/sinA

=[1+2cos²(A/2)-1]/[2sin(A/2)cos((A/2)]

=2cos²(A/2)/[2sin(A/2)cos((A/2)]

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

=cot(A/2)=右边

命题得证