等式sin^2x+sin2x-2cos^2x=m对一切x∈R成立,求m的取值范围.

题目

等式sin^2x+sin2x-2cos^2x=m对一切x∈R成立,求m的取值范围.
要详细过程.谢谢.

答案

sin^2x+sin2x-2cos^2x=mm=sin2x+sin^2x+cos^2x-3cos^2x=sin2x+1-3/2*(cos2x+1)=sin2x-3cos2x/2-3/2+1=sin2x-3/2cos2x-1/2因为√[(1^2+(3/2)^2]=√13/2所以m=√13/2 *1/(√13/2)*sin2x-(3/2)/(√13/2)cos2x)-1/2令1/(...