cos²x + cos²(x + pi/3) + cos²(x - pi/3) = 3/2. prove

LHS = Cos²x + Cos²(x+^/3) + Cos²(x-^/3)

  = (1+cosx)1/2 + (1+cos(x+^/3))1/2 + (1+cos(x-^/3)) 1/2 

  = 1/2 ( 1+cosx + 1 +Cos(x+^/3) + 1 + Cos(x-^/3)  )

  = 1/2 ( 3 + cosx + Cos( x + 60 ) + Cos( x - 60)

.  = 1/2 ( 3 + Cosx + 2 cosx cos120)

  = 1/2 ( 3 + cosx + 2 cosx . -1/2)  (since  cos 120 = -1/2)

  = 1/2 ( 3 + cosx - cosx)

  = 3/2 = RHS

  here , ^ means "pi"

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