已知 f(x)=cos (2x-派/3)+2sin (x-派/4)sin (x+派/4)
=cos (2x-派/3)-2sin (x+派/4-派/2)sin (x+派/4)
=cos (2x-派/3)-2cos (x+派/4)sin (x+派/4)
=cos (2x-派/3)+sin (2x+派/2)
=cos (2x-派/3)-cos 2x
根據(jù)和差化積的公式,得
原式=2sin (2x-派/6)sin (派/6)
=sin (2x-派/6)
周期T=2派/2=派,對(duì)稱(chēng)軸：2x-派/6=派/2+k派 (k屬于整數(shù))
x=派/3+k派/2 (k屬于整數(shù))
因?yàn)楹瘮?shù) f(x)在-派/6到派/3為單調(diào)增函數(shù)
所以函數(shù) f(x)在-派/12到派/2上的值域?yàn)椋篬-根號(hào)3/2,1]