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【三角函数证明求证:tan(45度+x/2)=cosx/(1+sinx)】
三角函数证明
求证:
tan(45度+x/2)=cosx/(1+sinx)
1回答
2020-01-2921:54
【三角函数证明求证:tan(45度+x/2)=cosx/(1+sinx)】
三角函数证明
求证:
tan(45度+x/2)=cosx/(1+sinx)
tan(π/4+x/2)
=[1+tan(x/2)]/[1-tan(x/2)]
=[cos(x/2)+sin(x/2)]/[cos(x/2)-sin(x/2)]
={[cos(x/2)]^2-[sin(x/2)]^2}/[cos(x/2)-sin(x/2)]^2
=cosx/(1-2sin(x/2)cos(x/2))
=cosx/(1-sinx)