①由于f(a)=cos(a-¼π)=7√2/10,∴sin2a=cos(½π-2a)=cos2(¼π-a)=2cos²(¼π-a)-1.
所以,将cos(a-¼π)=7√2/10代入,或者将cos(¼π-a)=7√2/10代入即可.
②g(x)=f(x)×f(x+π/2)=cos(x-¼π)cos(x+¼π)=cos(x-¼π)sin[½π-(x+¼π)]=
=cos(¼π-x)sin(¼π-x)=½sin2[(¼π-x)]=½sin(½π-2x)=½cos2x.
x∈[-π/6,π/3],∴2x∈[-π/3,π2/3].∴g(x)=f(x)×f(x+π/2)=½cos2x有左边的初始值½,经过最大值1,降低到最小值-½.