Question

方程sin^2x+4sinxcosx-2cons^2x=a有实数根,求a的取值范围

Answer 1

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]