方程sin^2x+4sinxcosx-2cons^2x=a有实数根,求a的取值范围
问题描述:
方程sin^2x+4sinxcosx-2cons^2x=a有实数根,求a的取值范围
答
sin^2x+4sinxcosx-2cos^2x=1-3cos^2x+2sin2x
=1-3(cos2x+1)/2+2sin2x=2sin2x-3cos2x/2-1/2
=√(4+9/4)*sin(2x+ψ)-1/2=a
a∈[-3,2]