Question

证明tanα/2=1-cosɑ/sinɑ

Answer 1

证明：
1-cosɑ/sinɑ
={1-[1-2sin²(α/2)]}/[2sin(ɑ/2)cos(ɑ/2)]
=2sin²(ɑ/2)/[2sin(ɑ/2)cos(ɑ/2)]
=sin(ɑ/2)/cos(ɑ/2)
=tan(α/2)
∴ tan(α/2)=(1-cosɑ)/sinɑ