(1)a·b=cos3x/2cosx/2-sin3x/2sinx/2=cos(3x/2+x/2)=cos2x
|a+b| =√[(cos3x/2+cosx/2)^2+(sin3x/2-sinx/2)^2]
=√[(cos3x/2)^2+(sin3x/2)^2+(cosx/2)^2+(sinx/2)^2+2cos3x/2cosx/2-2sin3x/2sinx/2]
=√(2+2(cos3x/2cosx/2-2sin3x/2sinx/2))
=√(2+2cos2x)
=√(2+2(cosx)^2-2(sinx)^2)
=√4(cosx)^2
=2cosx 因为x属于[0,π/2],所以cosx大于等于0,开根号不用加负号
(2)f(x)=2cos²x-1-2λ*2cosx
=2cos²x-4λ*cosx-1
对称轴x=λ
当λ≤-1即对称轴在[-1.1]左侧
f(x)在[-1,1]单增
f(x)min=f(-1)=2+4λ-1=-3/2
λ=-5/8>-1与题设矛盾,舍
当-1