Question

Prove that, cos2A=2cos×cosA-1

Answer 1

Answer:

Step-by-step explanation:

we know that Cos(A+B) = CosACosB - SinASinB. Thus

Cos2A = Cos(A+A)

            = CosACosA - SinASinA

             = Cos²A - Sin²A

             = Cos²A - (1 - Cos²A)    (∵ Sin²θ = 1 - Cos²θ)

             = 2Cos²A - 1.

             = R.H.S.

Hence proved