函数Y=SIN2XCOSX/(1-SINX)的值域是什么
我需要过程
參考答案:Y=SIN2XCOSX/(1-SINX)
=(2sinXcos^2 X)(1+sinX)/(1-sin^2 X)
=2sinX(1+sinX)
=2(sin^2 X+sinX)
=2(sin^2 X+sinX+1/4-1/4)
=2(sinX+1/2)^2-1/2
-1<=sinX<=1
-1/2<=sinX+1/2<=3/2
0<=(sinX+1/2)^2<=9/4
0<=2(sinX+1/2)^2<=9/2
-1/2<=2(sinX+1/2)^2-1/2<=4
当2(sinX+1/2)^2-1/2=4时 sinX=1 而1+sinX不等于0 所以sinX不等于0
也就是2(sinX+1/2)^2-1/2不等于4
综上所述函数Y=SIN2XCOSX/(1-SINX)的值域为-1/2<=2(sinX+1/2)^2-1/2<4