简化三角函数:csc(x)/sin(x)-(cot(x)csc(x))/sec(x)

来源：学生作业帮编辑：灵鹊做题网作业帮分类：数学作业时间：2024/04/30 23:49:01

csc(x)/sin(x)-(cot(x)csc(x))/sec(x)
=1/sin²(x) - sin(x)/cos(x) * 1/sin(x) * cos(x)
=1/sin²(x) -1
=(1-sin²(x))/sin²(x)
=cos²(x)/sin²(x)
=cot²(x)
哪一步不明白,可以追问!
再问：第一步的cot(x)为什么会变成sin(x)/cos(x)呢? 公式的cot(x)=cos(x)/sin(x)?
再答：写反了 csc(x)/sin(x)-(cot(x)csc(x))/sec(x) =1/sin²(x) - cos(x)/sin(x) * 1/sin(x) * cos(x) =1/sin²(x) - cos²(x)/sin²(x) =(1-cos²(x))/sin²(x) =sin²(x)/sin²(x) =1 这回对了还有问题么？
再问：谢谢你:)

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