Known vector a = (2cos square x, √ 3) B = (1, sin2x), function f (x) = a · B, find the minimum positive period and monotone increasing interval of (1) function f (x)

Known vector a = (2cos square x, √ 3) B = (1, sin2x), function f (x) = a · B, find the minimum positive period and monotone increasing interval of (1) function f (x)

From a = (2cos & # 178;; X, √ 3)
b=（1,sin2x）
f(x)=ab=2cos²;x+√3sin2x
=2(cos2x+1)/2+√3sin2x
=cos2x+√3sin2x+1
=2(1/2cos2x+√3/2sin2x)+1
=2(cos60°cos2x+sin60°sin2x)+1
=2cos(2x-60°)+1
(1) Minimum positive period T = 2 π / 2 = π
(2) When π / 3 + K π < x < 4 π / 3 + K π, it decreases monotonically,
When - 2 π / 3 + K π ＜ x ＜ π / 3 + K π, it increases monotonically