证明tanα/2=1-cosɑ/sinɑ

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证明tanα/2=1-cosɑ/sinɑ
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证明tanα/2=1-cosɑ/sinɑ
证明tanα/2=1-cosɑ/sinɑ

证明tanα/2=1-cosɑ/sinɑ
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

右边=2sin²(ɑ/2)/[2*sin(ɑ/2)*cos(ɑ/2)]
=sin(ɑ/2) / cos(ɑ/2)
=tan(ɑ/2)
=左边
所以等式得证。