2.设f(x)=(sin^4 x-cos^4 x-5)/(cos2x+2).(a)证明f(x)= 3/(2 sin^2 x-3) -1 (b)求f(x)的范围
问题描述：
2.设f(x)=(sin^4 x-cos^4 x-5)/(cos2x+2).(a)证明f(x)= 3/(2 sin^2 x-3) -1 (b)求f(x)的范围
答
f(x)=[(sin^2 x+cos^2 x)(sin^2 x-cos^2 x)-5]/[1-2sin^2 x+2]=(sin^2 x-cos^2 x-5)/[3-2sin^2 x]=(2sin^2 x-3-3)/[3-2sin^2 x]=3/(2 sin^2 x-3) -1得证当sin^2 x=1时,f(x)有最小值-4,当sin^2 x=0时,f(x)有最大值-2 ...