Question

已知函数fx=sin（2x加6分之派）+sin（2x-6分之派）+cos2x+a 若x属于［0,二分

Answer 1

f(x)=sin(2x+π/6)+sin(2x-π/6)+cos2x+a

=√3/2sin2x+1/2cos2x+√3/2sin2x-1/2cos2x+cos2x+a

=√3sin2x+cos2x+a

=2sin(2x+π/6)+a

x∈[0,π/2] ,则2x+π/6∈[π/6,7π/6]

sin(2x+π/6)的最小值是sin(7π/6)=-1/2

所以2*(-1/2)+a=-2

a=-1