①由于f(a)＝cos(a－¼π)＝7√2/10,∴sin2a＝cos(½π－2a)＝cos2(¼π－a)＝2cos²(¼π－a)－1.
所以,將cos(a－¼π)＝7√2/10代入,或者將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有左邊的初始值½,經(jīng)過最大值1,降低到最小值－½.