f(x)=sin2x-2根号3cos^2x+根号3x属于45度,90度求f（x）的最大值最小值

Question

f(x)=sin2x-2根号3cos^2x+根号3 x属于【45度,90度】 求f（x）的最大值最小值

Answer 1

f(x)=sin2x-2根号3cos^2x+根号3
= sin2x - 2根号3 * [(cos2x +1)/2] + 根号3
= sin2x - 根号3 cos2x - 根号3 + 根号3
= sin2x - 根号3 cos2x
=2(sin2xcos60°-cos2xsin60°)
=2sin(2x-60°)
45° ≤ x ≤ 90°
30° ≤ 2x-60° ≤ 120°
2x-60°=90°时有最大值：f(75°)=2
2x-60°=30°时有最小值：f(45°)=1