化简函数f(x)=cos2x/sin(45'-x)
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/28 20:57:14
化简函数f(x)=cos2x/sin(45'-x)
f(x)=cos2x/sin(45°-x)
= (cos^2x-sin^2x)/(sin45°cosx-cos45°sinx)
= (cosx+sinx)(cosx-sinx) / [√2/2(cosx-sinx)]
= √2(cosx+sinx)
= 2(sinxcos45°+cosxsin45°)
= 2sin(x+45°)
= (cos^2x-sin^2x)/(sin45°cosx-cos45°sinx)
= (cosx+sinx)(cosx-sinx) / [√2/2(cosx-sinx)]
= √2(cosx+sinx)
= 2(sinxcos45°+cosxsin45°)
= 2sin(x+45°)
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