化简函数f(x)=cos2x/sin(45'-x)

化简函数f(x)=cos2x/sin(45'-x)
化简函数f(x)=cos2x/sin(45'-x)

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°)

2sin(x+45°)

也可以这样
f(x)=sin(90-2x)/sin(45-x)
=2sin(45-x)cos(45-x)/sin(45-x)
=2cos(45-x)

cos2x/sin(45'-x)=(cosx-sinx)(cosx+sinx)/(√2／2(cosx-sinx))=√2(cosx+sinx)