已知函数f(x)=1/2cos2x+根号3sinxcosx-2cos^2x
问题描述:
已知函数f(x)=1/2cos2x+根号3sinxcosx-2cos^2x
(1)求f(x)的最大值 (2)若f(a)=-1/5,求cos(2a+π/3) (3)若π/3
答
f(x)=1/2cos2x+根号3/2sin2x-1-cos2x =√3/2 ×sin2x-1/2 ×cos2x -1 =sin(2x-π/6) -1当sin(2x-π/6)=1时f(x)有最大值=0f(a)=-1/5则,sin(2a-π/6)-1=-1/5sin(2a-π/6)=4/5所以,cos(2a+π/3)=cos(2a...