Question

向量OP=(2COSX+1.COS2X-SINX+1),向量OQ=(COSX,-1),f(X)=OP*OQ,f(X)的最

Answer 1

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取到最大,y=√2

,f(X)的最大值及取得最大值时的x的取值集合{x|x=2kπ+π/4}