F(*)=根号3sin2*-cos2*+1 ,求最小值

问题描述:

F(*)=根号3sin2*-cos2*+1 ,求最小值

f(x)=2(√3/2sin2x-1/2cos2x)+1
=2(sin2xcosπ/6-cos2xsinπ/6)+1
=2sin(2x-π/6)+1
sin(2x-π/6)最小=-1
所以f(x)最小值=2×(-1)+1=-1