How 1 + Cos (2A) = 2 Cos²A ?

How Cos (2A) = 2 Cos²A - 1 ?

As we know that

 ➡ Cos(2A) = Cos²A - Sin²A.......(1)

Also Sin²A + Cos²A = 1

 or Sin²A = 1 - Cos²A......[put in (1) eq.]

➡Cos (2A) = Cos²A - (1 - Cos²A)

                = Cos²A - 1 + Cos²A

Hence, 

          Cos (2A) = 2 Cos²A - 1

         or 1 + Cos(2A) = 2 Cos²A

➡If angle is half i.e. θ = A

then, Cos (A) = 2 Cos²(A/2) - 1

      or 1 + Cos(A) = 2 Cos²(A/2)