sin^2x+2sinx+3cos^2x怎么化简
问题描述：
sin^2x+2sinx+3cos^2x怎么化简
答
随便就出来了
答
sin^2x+2sinx+3cos^2x
原式=3-2sin^2x+2sinx
=3-2sinx(sinx-1)
=-2(sinx-1/2)^2+7/2
答
中间应该是2sinxcosx
原式=(sin²x+cos²x)+sin2x+2cos²x-1+1
=1+sin2x+cos2x+1
=√2(√2/2*sin2x+√2/2cos2x)+2
=√2(sin2xcosπ/4+cos2xsinπ/4)+2
=√2sin(2x+π/4)+2