求证:(1+sinα)/cosα=(1+tanα/2)/(1-tanα/2)
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求证:(1+sinα)/cosα=(1+tanα/2)/(1-tanα/2)
证明:sina=sin(a/2*2)=s*sin(a/2)*cos(a/2)
cosa=cos(a/2*2)=(cos(a/2))^2-(sin(a/2))^2
把sina,cosa代入:(1+sinα)/cosα=(sin(a/2)+cos(a/2))^2/(sin(a/2)-cos(a/2))/(sin(a/2)+cos(a/2))
=(sin(a/2)+cos(a/2))/(sin(a/2)-cos(a/2))
=(1+tan(a/2))/(1-tan(a/2))
cosa=cos(a/2*2)=(cos(a/2))^2-(sin(a/2))^2
把sina,cosa代入:(1+sinα)/cosα=(sin(a/2)+cos(a/2))^2/(sin(a/2)-cos(a/2))/(sin(a/2)+cos(a/2))
=(sin(a/2)+cos(a/2))/(sin(a/2)-cos(a/2))
=(1+tan(a/2))/(1-tan(a/2))
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