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化简函数f(x)=cos2x/sin(45'-x)

题目详情
化简函数f(x)=cos2x/sin(45'-x)
▼优质解答
答案和解析
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°)