= 2sinωxcosωx -√3(2cos？ ωx - 1) +m

Sine and cosine formulas with twice the angle are used here.

= sin2ωx - √3 cos2ωx +m

= 2[( 1/2)sin 2ωx-(√3/2)cos 2ωx]+m

= 2 (sin2ωxcos60 - cos2ωxsin60 ] +m

= 2 sin(2ωx-60 ) +m

As can be seen from the figure, the average of the maximum value and the minimum value is 2, so m=2.

You can understand other estimates.

(2)f(x)=2sin(3x-60 )+2

Move π/9 to the left by 1 unit to obtain:

g(x)= 2 sin 3(x+π/9)-π/3+2- 1

= 2sin3x + 1