Why are second kind Chebyshev points the first kind extrema?

[MikaelSlevinsky]

julia> n = 10
10

julia> pts = chebyshevpoints(Float64, n+1, Val(2))
11-element FastTransforms.ChebyshevGrid{2, Float64}:
  1.0
  0.9510565162951536
  0.8090169943749475
  0.5877852522924731
  0.30901699437494745
  0.0
 -0.30901699437494745
 -0.5877852522924731
 -0.8090169943749475
 -0.9510565162951536
 -1.0

julia> cos.(n.*acos.(pts))
11-element Vector{Float64}:
  1.0
 -1.0
  1.0
 -1.0
  1.0
 -1.0
  1.0
 -1.0
  1.0
 -1.0
  1.0

Shouldn't they be the roots of the second kind Chebyshev polynomials?