证明:tan(x/2)=sinx/1+cosx

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证明:tan(x/2)=sinx/1+cosx

证明:tan(x/2)=sinx/1+cosx
证明:tan(x/2)=sinx/1+cosx

证明:tan(x/2)=sinx/1+cosx
tan(x/2)
= sin(x/2) / cos(x/2)
= 2sin(x/2) cos(x/2) / [ 2cos²(x/2) ]
= sinx / (1+cosx)

tan(x/2)=sin(x/2)/cos(x/2)=(2sin(x/2)cos(x/2))/(2(cos(x/2))^2)=sinx/(cosx+1)
因为cosx=2(cos(x/2))^2-1,sinx=2sin(x/2)cos(x/2)