y=sin²X+2sinXcosX-3cos²X
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y=sin²X+2sinXcosX-3cos²X
![y=sin²X+2sinXcosX-3cos²X](/uploads/image/z/19863530-26-0.jpg?t=y%3Dsin%26%23178%3BX%2B2sinXcosX-3cos%26%23178%3BX)
y=sin²x+2sinxcosx-3cos²x
=(sin²x+cos²x)+2sinxcosx-4cos²x
=1+2sinxcosx-4cos²x
=1+sin(2x)-2[cos(2x)+1]
=sin2x-2cos2x-1
如果是:y=sin²x+2sinxcosx+3cos²x
=(sin²x+cos²x)+2sinxcosx+2cos²x
=1+2sinxcosx+2cos²x
=1+sin(2x)+1+cos(2x)
=(√2)[(√2/2)sin(2x)+(√2/2)cos(2x)]+2
=(√2)[cos(π/4)sin(2x)+sin(π/4)cos(2x)]+2
=(√2)sin(2x+π/4)+2
=(sin²x+cos²x)+2sinxcosx-4cos²x
=1+2sinxcosx-4cos²x
=1+sin(2x)-2[cos(2x)+1]
=sin2x-2cos2x-1
如果是:y=sin²x+2sinxcosx+3cos²x
=(sin²x+cos²x)+2sinxcosx+2cos²x
=1+2sinxcosx+2cos²x
=1+sin(2x)+1+cos(2x)
=(√2)[(√2/2)sin(2x)+(√2/2)cos(2x)]+2
=(√2)[cos(π/4)sin(2x)+sin(π/4)cos(2x)]+2
=(√2)sin(2x+π/4)+2
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