sin^2x+2sinx+3cos^2x怎么化简

题目

sin^2x+2sinx+3cos^2x怎么化简

答案

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