化简y=sin^2(x)+2sin(x)cos(x)+3cos^2(x)

题目

化简y=sin^2(x)+2sin(x)cos(x)+3cos^2(x)

答案

y=sin²x+2sinxcosx+3cos²x
y=(sin²x+cos²x)+2sinxcosx+(2cos²x-1)+1
=1+sin2x+cos2x+1
=√2sin(2x+π/4)+2