f(x)

=cos？ x-sin？ x+2√3sinxcosx

=cos2x+√3sin2x

= 2[( 1/2)cos2x+(√3/2)sin2x]

=2sin(2x+π/6)

1, the minimum positive period of the function f(x) is π,

2kπ+π/2≤2x+π/6≤2kπ+3π/2

The monotone decreasing interval is [kπ+π/6, kπ+2π/3];

2. Now the ordinate is reduced to 1/2 times, and the abscissa remains unchanged.

Then the abscissa is expanded to twice the original, and the ordinate is unchanged.

Finally, shift π/3 units to the left.

3、f(A)= 1

sin(2x+π/6)= 1/2

2x+π/6=π/6+2kπ

x=kπ

2x+π/6=5π/6+2kπ

2x=2π/3+2kπ

x=π/3+kπ

∫A is the inner angle of a triangle.

∴A=π/3

∴ From cosine theorem A2 = B2+C2-2bcosa: 3 = B2+C2-BC = (b+c) 2-3bc.

∴(b+c)2-3=3bc≤3？ [(b+c)/2] 2, take the equal sign if and only if b=c,

∴ (b+c) 2/4 ≤ 3, that is, (b+c) 2 ≤ 12.

∴0