How Cos(2A) = Cos²A - Sin²A or Cos(A) = Cos²(A/2) - Sin²(A/2) ?

Derivation of Cos(2A) = Cos²A - Sin²A

or

Cos(A) = Cos²(A/2) - Sin²(A/2)?

As we know that,

Cos(A+B) = CosA CosB - SinA SinB

........👉👉{Cos(A+B) = CosA CosB - SinA SinB}

put B= A 

we get,

⇒Cos(A+A) = CosA CosA - SinA SinA

⇒Hence, Cos(2A) = Cos²A - Sin²A

⇒If angle will be halved i.e. θ = A

Then,

     ⇒ Cos(A) = Cos²(A/2) - Sin²(A/2)