求f(x)=cosxsinx+1/cosxsinx-1的值域

y=(cosxsinx+1)/(cosxsinx-1)
=(cosxsinx+(sinx)^2+(cosx)^2)/(cosxsinx-(sinx)^2-(cosx)^2)
=((tgx)^2+tgx+1)/(tgx-(tgx)^2-1)
y(tgx-(tgx)^2-1)=(tgx)^2+tgx+1
(1+y)(tgx)^2+(1-y)tgx+(1+y)=0
此方程可看作tgx的二次方程，有实根的条件是:
(1-y)^2-4(1+y)(1+y)>=0
(3y+1)(y+3)<=0
-3<=y<=-1/3
f(x)=cosxsinx+1/cosxsinx-1的值域:[-3,-1/3]

设y=f(x)=(cosxsinx+1)/(cosxsinx-1)
=(cosxsinx+(sinx)^2+(cosx)^2)/(cosxsinx-(sinx)^2-(cosx)^2)
=((tgx)^2+tgx+1)/(tgx-(tgx)^2-1)
y(tgx-(tgx)^2-1)=(tgx)^2+tgx+1
(1+y)(tgx)^2+(1-y)tgx+(1+y)=0
看作tgx的二次方程，有实根的条件是:
(1-y)^2-4(1+y)(1+y)>=0
(3y+1)(y+3)<=0
-3<=y<-1/3和y=-1/3
f(x)=cosxsinx+1/cosxsinx-1的值域:[-3,-1/3]