(cosx+sinx)平方+根号3倍cos2x-1在区间(O,π/2)的最大值和最小值

问题描述:

(cosx+sinx)平方+根号3倍cos2x-1在区间(O,π/2)的最大值和最小值

(cosx+sinx)平方+根号3倍cos2x-1
=cos²x+sin²x+sin2x+√3cos2x-1
=sin2x+√3cos2x
=2sin(2x+π/3)
π/3x=π/12 最大值2
x=π/2 最小值-√3

y=(sinx+cosx)²+√3cos2x-1
=sin²x+cos²x+2sinxconx+√3cos2x-1
=1+sin2x+√3cos2x-1
=2sin(2x+π/3)
0