How 1 - Cos(2A) = 2Sin²A?

How 1 - Cos2A = 2 sin²A?

As we know that,

Cos(2A) = Cos²A - Sin²A.........(1)

........👉{Cos(2A) = Cos²A - Sin²A}

also, Sin²A + Cos²A = 1

      or Cos²A = 1- Sin²A......(2)

...............👉{How Sin²θ + Cos²θ = 1??}

put eq. (2) into eq.(1)

Cos(2A) = 1 - Sin²A - Sin²A

Hence, Cos(2A) = 1 - Sin²A

also, 1 - Cos2A = 2 sin²A

 If angle(ϴ) is halved,

then,

CosA = 1 - Sin²(A/2)

or 

1 - CosA = 2 sin²(A/2)