f(x)=2sin^2((π/4)+x)-(根号3)(cos2x),x∈[π/4,π/2]..

题目

f(x)=2sin^2((π/4)+x)-(根号3)(cos2x),x∈[π/4,π/2]..
求f(x)单调区间

答案

f(x) = [sin(x) + cos(x)]^2 - 3^(1/2)cos(2x)
= 1 + sin(2x) - 3^(1/2)cos(2x)
= 1 + 2[sin(2x)/2 - 3^(1/2)cos(2x)/2]
= 1 + 2sin(2x - π/3)
π/4