高中数学题 三角比 三角函数

f(x)=(cos2x+1)/2+(√3/2)sin2x+a
=(cos2x+√3sin2x)/2+a+1/2
=√[(√3)^2+1^2]sin(2x+arctan1/√3)+a+1/2
=2sin(2x+π/6)+a+1/2
√为根号的意思。
因为0<=x<=π/2
则0<=2x<=π
所以π/6<=2x+π/6<=7π/6
所以2x+π/6=7π/6时sin(2x+π/6)最小=-1/2
f(x)最小=2*(-1/2)+a+1/2=2
所以a-1/2=2
即a=5/2

是暑假作业上的吧？

f(x)=(cos2x+1)/2+(√3/2)sin2x+a
=(cos2x+√3sin2x)/2+a+1/2
=√[(√3)^2+1^2]sin(2x+arctan1/√3)+a+1/2
=2sin(2x+π/6)+a+1/2

0<=x<=π/2
0<=2x<=π
π/6<=2x+π/6<=7π/6
所以2x+π/6=7π/6时sin(2x+π/6)最小=-1/2
f(x)最小=2*(-1/2)+a+1/2=2
a-1/2=2
a=5/2