f(x)=sin(2x+π/6)+cos(2x-5π/3)+sin2x 1.求f（x）的最小正周期和单调区间

题目

f(x)=sin(2x+π/6)+cos(2x-5π/3)+sin2x 1.求f（x）的最小正周期和单调区间
2.若三角形ABC中 f（A/2）=根号2 a=2 b=根号6 求角C

答案

(1)f(x)=sin(2x+π/6)+cos(2x-5π/3)+sin2x =sin2xcosπ/6+cos2xsinπ/6+cos2xcos5π/3+sin2xsin5π/3+sin2x=√3/2sin2x+1/2cos2x+1/2cos2x-√3/2sin2x+sin2x=sin2x+cos2x=√2(√2/2sin2x+√2/2cos2x)=√2sin(2x+π/...