1+sinx+cosx化为积的形式是

1+sinx+cosx化为积的形式是
1+sinx+cosx化为积的形式是

1+sinx+cosx化为积的形式是
公式：
sin2x = 2sinxcosx
cos2x = 2cos²x - 1 = 1 - 2sin²x
∴1 + sinx + cosx
= (1 + cosx) + sinx
= 2cos²(x/2) + 2sin(x/2)cos(x/2)
= 2cos(x/2) * [cos(x/2) + sin(x/2)]
= 2cos(x/2) * √2sin(x/2 + π/4)
= 2√2 * sin(x/2 + π/4)cos(x/2)