1.
y=sin²x+2sinxcosx-3cos²x+a
=sin²x-cos²x+2sinxcosx-2cos²x+a
=sin²x-cos²x+2sinxcosx-2cos²x+1-1+a
=﹣cos2x+sin2x-(2cos²x-1)-1+a
=﹣cos2x+sin2x-cos2x-1+a
=sin2x - 2cos2x+a-1
=√5sin(2x+α)+a-1 (其中sinα=-2/√5= -2√5/5,cosα=√5/5)
∴T=2π/2=π
2.
y=√5sin(2x+α)+a-1=-1
a=-√5sin(2x+α)
∵sin(2x+α)∈[-1,1]
∴a∈[-√5,√5]