1.
f(x)=√ 3sin2x+2cos²x+3
= √ 3sin2x + cos2x + 1 + 3
= √ √10sin(2x + θ）+ 4（tanθ = 1/3)
∵ x属于（0,π/2）∴ θ < 2x + θ < π+θ
∴ f(x)max = √ √ 10+ 4
f(x)min = √ 3
2. 根据已知条件,无解.
解题思路：先求出 sin(2x + θ)的值,在求出 sin2x 和 cos2x的值,最后求出 cos（2x-π/12)的值