Question

已知函数y=1/2cos^x+/2 sinxcosx+1，x属于R，怎么化简

Answer 1

是否题目为：
y=1/2*cos^2(x)+1/2 *sinxcosx+1
=1/4(1+cos2x)+1/4 sin2x+1
=1/4(sin2x+cos2x+5/4
=√2/4(√2/2 sin2x+√2/2 cos2x)+5/4
=√2/4sin(2x+π/4)+5/4

Answer 2

y=(1/2)cos²x+(√3/2)sinxcosx+1
=(1/4)[1+cos(2x)]+(√3/4)(2sinxcosx)+1
=(1/4)cos(2x)+(√3/4)sin(2x)+5/4
=½[(1/2)cos(2x)+(√3/2)sin(2x)]+5/4
=½cos(2x-π/3)+5/4

Answer 3

y=1/2cos^2x+1/2 sinxcosx+1
＝1/4(1+cos2x+1/4 sin2x+1
=√2/4(√2/2cos2x+√2/2 sin2x)+5/4
=√2/4sin(2x+π/4)+5/4