向量OP=(2COSX+1.COS2X-SINX+1),向量OQ=(COSX,-1),f(X)=OP*OQ,f(X)的最大值及取得最大值时的x的取值集合

问题描述:

向量OP=(2COSX+1.COS2X-SINX+1),向量OQ=(COSX,-1),f(X)=OP*OQ,f(X)的最大值及取得最大值时的x的取值集合

f(x)=cosx(2cosx+1)-(cos2x-sinx+1) =2(cosx)^2+cosx-cos2x+sinx-1 =2(cosx)^2-1-cos2x+cosx+sinx =cos2x-cos2x+cosx+sinx =sinx+cosx =√2[√2sinx/2+√2cosx/2] =√2sin(x+π/4) x+π/4=2kπ+π/2 x=2kπ+π/4时,y...