(1)
f(cosx)＝f[sin(π/2-x)]
＝cos2(π/2-x)+sin(π/2-x)
＝cos(π-2x)+sin(π/2-x)
＝-cos2x+cosx.
(2)
f(sinx)+f(cosx)
＝(cos2x+sinx)+(-cos2x+cosx)
＝sinx+cosx
＝√2[sinx·(√2/2)+cosx·(√2/2)]
＝√2(sinx·cos45°+cosx·sin45°)
＝√2sin(x+45°),
∴sin(x+45°)＝1时,最大值为√2；
sin(x+45°)＝-1时,最小值为-√2.