已知向量a=(cos3x,sin3x),b=(cosx,-sinx),且x∈[0,π/4],求f(_百度...答:a*b=cos3xcosx-sin3xsinx=cos4x,|a|=|b|=1,(a+b)^2=a^2+2a*b+b^2=2+2cos4x=4(cos2x)^2,2x∈[0,π/2],∴|a+b|=2cos2x,∴f(x)=λcos4x-2λcos2xsin2x=λ(cos4x-sin4x)=λ√2cos(4x+π/4),x∈[0,π/4],u=4x+π/4的值域是[π/4,5π/4],v=cosu在[π...