f(x)=cos2x/cos(π/4+x)=(cos²x-sin²x)/(√2/2cosx-√2/2sinx)=(cosx+sinx)(cosx-sinx)/[√2/2(cosx-sinx)]=√2(cosx+sinx)=2(√2/2cosx+√2/2sinx)=2sin(x+π/4)