exact value of cos ?/12

Question

Use a half angle identity to find the exact value of Cos Π/12

Answer 1

 Cos 2X = 2 Cos^2X -1

 

  Let X = ∏/12

 

   Cos ∏ /6 = 2 Cos ^2 ∏/12 -1 

 

    √(3)  /2 = 2 Cos ² ∏/12 -1

 

     Cos ² ∏/12  = 1/2 ( √(3) /2 +1)= √3 / 4 + 1/2

 

      Cos ∏/12 = √((√3)/4 +1/2)

                    = 0.965925826

        Cos ∏/12 = 0.965625826 ( from Calculator) .