已知向量m=(cosx,-sinx),n=(cosx,sinx-2根号3cosx),x属于R,设f(x)=m*n

问题描述:

已知向量m=(cosx,-sinx),n=(cosx,sinx-2根号3cosx),x属于R,设f(x)=m*n

f(x)
=m.n
=(cosx,-sinx).(cosx,sinx-2√3cosx)
=(cox)^2- (sinx)^2 + 2√3sinxcosx
= cos2x + √3sin2x
= 2( (1/2)cos2x + √3/2 sin2x)
= 2( sin(2x+π/6)