(1+sinx+cosx)/(sinx/2+cosx/2)化简
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/14 13:58:16
(1+sinx+cosx)/(sinx/2+cosx/2)化简
化简
(1+sinx+cosx)/(sinx/2+cosx/2)
化简
(1+sinx+cosx)/(sinx/2+cosx/2)
分子=[sin²(x/2)+cos²(x/2)]+2sin(x/2)cos(x/2)+[cos²(x/2)-sin²(x/2)]
=[cos(x/2)+sin(x/2)]²+[cos(x/2)-sin(x/2)][cos(x/2)+sin(x/2)]
=[cos(x/2)+sin(x/2)][cos(x/2)+sin(x/2)+cos(x/2)-sin(x/2)]
=[cos(x/2)+sin(x/2)][2cos(x/2)]
分母=cos(x/2)+sin(x/2)
所以原式=2cos(x/2)
=[cos(x/2)+sin(x/2)]²+[cos(x/2)-sin(x/2)][cos(x/2)+sin(x/2)]
=[cos(x/2)+sin(x/2)][cos(x/2)+sin(x/2)+cos(x/2)-sin(x/2)]
=[cos(x/2)+sin(x/2)][2cos(x/2)]
分母=cos(x/2)+sin(x/2)
所以原式=2cos(x/2)
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