已知对任意α∈R,m=cos2(α-3/π)+cos2α+cos(α+3/π)为常数,则m=错了是π/3

Question

已知对任意α∈R,m=cos2(α-3/π)+cos2α+cos(α+3/π)为常数,则m=
错了 是π/3

Answer 1

m=cos2(a-π/3)+cos2a+cos2(a+π/3)
=cos(2a-2π/3)+cos2a+cos(2a+2π/3)
=cos2acos2π/3+sin2asin2π/3+cos2a+cos2acos2π/3-sin2asin2π/3
=-cos2a/2+cos2a-cos2a/2
=0