(1)f(x)= sin x cos x+ √3 cos ² x+ √3 / 2
= (1 / 2)2 sin x cos x + √3 / 2 (2 cos ² x - 1)
= (1 / 2)sin 2x+ (√3 / 2)cos 2x
= sin 2x cos π / 3+ sin π / 3cos 2x
= sin(2 x + π / 3)
∴ 最小正周期为:T = 2 π / ω
= 2 π / 2
= π
(2)f(x)单调递减区间为: 【 k π + π / 12 ,k π + 7 π / 12 】
