高3数学联赛

y=tan(x+2π/3)+cot(x+2π/3)+cos(x+π/6)
=1/[cos(x+2π/3)sin(x+2π/3)]+cos(x+π/6)
=2/sin(2x+4π/3)+cos(x+π/6)

因为-5π/12≤x≤-π/3,
所以2x+4π/3∈[π/2,2π/3],
x+π/6∈[-π/4,-π/6],
可见2/sin(2x+4π/3)与cos(x+π/6)在定义域内同为递增函数,
故当x=-π/3时,y取最大值11√3/6